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C2×D9519 #49185176

order38076
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD19038
direct productC2×D9519
unambiguous semidirect product(C2×C3)⋊D3173
unambiguous semidirect product(C2×C19)⋊D501
unambiguous semidirect product(C2×C167)⋊D57

Splittings

Fitting, socleC2×C3×C19×C167 ⋊ C2
derived, HallC3×C19×C167 ⋊ C22
HallC19×C167 ⋊ C2×D3
HallC3×C167 ⋊ C2×D19
SylowC167 ⋊ C2×D57
HallC3×C19 ⋊ C2×D167
SylowC19 ⋊ C2×D501
SylowC3 ⋊ C2×D3173

Subgroups

subgroupG/H
center, hypercenterC2D9519
commutator, cosocle, hypocenterC3×C19×C167C22
FrattiniC1G
Fitting, socleC2×C3×C19×C167C2
LCSG ▷ C3×C19×C167
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 191
transitive degreeμt(G) = 19038

A minimal faithful permutation representation — 2 generators on 191 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);(4,5)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(26,191)(27,190)(28,189)(29,188)(30,187)(31,186)(32,185)(33,184)(34,183)(35,182)(36,181)(37,180)(38,179)(39,178)(40,177)(41,176)(42,175)(43,174)(44,173)(45,172)(46,171)(47,170)(48,169)(49,168)(50,167)(51,166)(52,165)(53,164)(54,163)(55,162)(56,161)(57,160)(58,159)(59,158)(60,157)(61,156)(62,155)(63,154)(64,153)(65,152)(66,151)(67,150)(68,149)(69,148)(70,147)(71,146)(72,145)(73,144)(74,143)(75,142)(76,141)(77,140)(78,139)(79,138)(80,137)(81,136)(82,135)(83,134)(84,133)(85,132)(86,131)(87,130)(88,129)(89,128)(90,127)(91,126)(92,125)(93,124)(94,123)(95,122)(96,121)(97,120)(98,119)(99,118)(100,117)(101,116)(102,115)(103,114)(104,113)(105,112)(106,111)(107,110)(108,109)

Conjugacy classes & character table

9522 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38076, 34);