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C2×D12699 #72288565

order50796
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD25398
direct productC2×D12699

Splittings

FittingC2×C9×C17×C83 ⋊ C2
derived, HallC9×C17×C83 ⋊ C22
HallC17×C83 ⋊ C2×D9
HallC9×C83 ⋊ C2×D17
HallC9×C17 ⋊ C2×D83
SylowC83 ⋊ C2×D153
SylowC17 ⋊ C2×D747
SylowC9 ⋊ C2×D1411

Subgroups

subgroupG/H
center, hypercenterC2D12699
commutator, cosocle, hypocenterC9×C17×C83C22
FrattiniC3C2×D4233
FittingC2×C9×C17×C83C2
socleC2×C3×C17×C83D3
LCSG ▷ C9×C17×C83
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 111
transitive degreeμt(G) = 25398

A minimal faithful permutation representation — 2 generators on 111 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);(4,11)(5,10)(6,9)(7,8)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(30,111)(31,110)(32,109)(33,108)(34,107)(35,106)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)

Conjugacy classes & character table

12702 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((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), (4,11)(5,10)(6,9)(7,8)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(30,111)(31,110)(32,109)(33,108)(34,107)(35,106)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71));