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C2×D6567 #39911089

order26268
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13134
direct productC2×D6567
unambiguous semidirect product(C2×C3)⋊D2189
unambiguous semidirect product(C2×C11)⋊D597
unambiguous semidirect product(C2×C199)⋊D33

Splittings

Fitting, socleC2×C3×C11×C199 ⋊ C2
derived, HallC3×C11×C199 ⋊ C22
HallC11×C199 ⋊ C2×D3
HallC3×C199 ⋊ C2×D11
SylowC199 ⋊ C2×D33
HallC3×C11 ⋊ C2×D199
SylowC11 ⋊ C2×D597
SylowC3 ⋊ C2×D2189

Subgroups

subgroupG/H
center, hypercenterC2D6567
commutator, cosocle, hypocenterC3×C11×C199C22
FrattiniC1G
Fitting, socleC2×C3×C11×C199C2
LCSG ▷ C3×C11×C199
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 215
transitive degreeμt(G) = 13134

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

Conjugacy classes & character table

6570 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD26268
maximal normal subgroup ofD26268
maximal quotient ofDic13134, D26268

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26268, 49);