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C2×D3345 #27211446

order13380
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD6690
direct productC2×D3345
unambiguous semidirect product(C2×C3)⋊D1115
unambiguous semidirect product(C2×C5)⋊D669
unambiguous semidirect product(C2×C223)⋊D15

Splittings

Fitting, socleC2×C3×C5×C223 ⋊ C2
derived, HallC3×C5×C223 ⋊ C22
HallC5×C223 ⋊ C2×D3
HallC3×C223 ⋊ C2×D5
SylowC223 ⋊ C2×D15
HallC3×C5 ⋊ C2×D223
SylowC5 ⋊ C2×D669
SylowC3 ⋊ C2×D1115

Subgroups

subgroupG/H
center, hypercenterC2D3345
commutator, cosocle, hypocenterC3×C5×C223C22
FrattiniC1G
Fitting, socleC2×C3×C5×C223C2
LCSG ▷ C3×C5×C223
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 233
transitive degreeμt(G) = 6690

A minimal faithful permutation representation — 2 generators on 233 points:

(1,2)(3,4,5)(6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233);(4,5)(7,10)(8,9)(12,233)(13,232)(14,231)(15,230)(16,229)(17,228)(18,227)(19,226)(20,225)(21,224)(22,223)(23,222)(24,221)(25,220)(26,219)(27,218)(28,217)(29,216)(30,215)(31,214)(32,213)(33,212)(34,211)(35,210)(36,209)(37,208)(38,207)(39,206)(40,205)(41,204)(42,203)(43,202)(44,201)(45,200)(46,199)(47,198)(48,197)(49,196)(50,195)(51,194)(52,193)(53,192)(54,191)(55,190)(56,189)(57,188)(58,187)(59,186)(60,185)(61,184)(62,183)(63,182)(64,181)(65,180)(66,179)(67,178)(68,177)(69,176)(70,175)(71,174)(72,173)(73,172)(74,171)(75,170)(76,169)(77,168)(78,167)(79,166)(80,165)(81,164)(82,163)(83,162)(84,161)(85,160)(86,159)(87,158)(88,157)(89,156)(90,155)(91,154)(92,153)(93,152)(94,151)(95,150)(96,149)(97,148)(98,147)(99,146)(100,145)(101,144)(102,143)(103,142)(104,141)(105,140)(106,139)(107,138)(108,137)(109,136)(110,135)(111,134)(112,133)(113,132)(114,131)(115,130)(116,129)(117,128)(118,127)(119,126)(120,125)(121,124)(122,123)

Conjugacy classes & character table

3348 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD13380
maximal normal subgroup ofD13380
maximal quotient ofD13380, Dic6690

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13380, 34);