#41001747

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
Hall	C₁₁²⋊C₃ ⋊ D₃₇
Sylow	C₁₁² ⋊ C₃×D₃₇
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:

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

Polycyclic presentation:

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

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26862, 21);