#41001745

order	26862
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₁²×C₃₇ ⋊ C₂×C₃
Hall	C₃₇⋊(C₁₁²⋊C₃) ⋊ C₂
Hall	C₁₁⋊D₄₀₇ ⋊ C₃
Sylow	C₁₁² ⋊ D₃₇⋊C₃
Sylow	C₃₇ ⋊ (C₁₁⋊D₁₁)⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₃₇	C₂×C₃
LCS	G ▷ C₁₁²×C₃₇
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 1221

A minimal faithful permutation representation — 2 generators on 70 points:

(2,6,7,3,4,8)(5,14,15,9,10,23)(11,26,27,17,18,34)(12,25,21,19,16,13)(20,36,37,29,28,32)(22,24,35,31,30,33)(38,39,41)(40,43,48,44,45,53)(42,61,63,49,50,67)(46,54,62,56,57,65)(47,66,51,59,58,55)(52,68,69,64,60,70);(1,2,5,11,18,28,33,34,31,21,7,6,12,20,30,10,16,23,32,37,15,25,14,24,29,19,4,8,13,22,27,35,36,26,17,9,3)(38,40,46,58,67,70,69,63,66,56,44)(39,42,51,43,52,57,54,64,45,55,49)(41,47,60,65,48,61,50,53,62,68,59)

Polycyclic presentation:

2,3,11^2,37|c^a=c^10,d^a=d^10,e^a=e^36,c^b=c^3d^9,d^b=cd^7,e^b=e^26

Conjugacy classes & character table

752 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26862, 19);