#44530205

order	31218
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₁²×C₄₃ ⋊ C₂×C₃
Hall	C₄₃×C₁₁²⋊C₃ ⋊ C₂
Hall	C₁₁⋊D₄₇₃ ⋊ C₃
Hall	C₁₁²⋊C₃ ⋊ D₄₃
Sylow	C₁₁² ⋊ C₃×D₄₃
Sylow	C₄₃ ⋊ (C₁₁⋊D₁₁)⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₄₃	C₂×C₃
LCS	G ▷ C₁₁²×C₄₃
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 76
transitive degree	μ_t(G) = 1419

A minimal faithful permutation representation — 2 generators on 76 points:

(1,2,4)(3,15,16,7,6,10)(5,24,19,11,12,29)(8,25,26,18,17,23)(9,30,28,20,21,14)(13,31,32,27,22,33)(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);(1,3,8,19,30,33,32,21,29,18,7)(2,5,13,25,6,14,28,15,17,27,11)(4,9,12,10,22,26,23,31,16,24,20)(34,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36)

Polycyclic presentation:

2,3,11^2,43|c^a=c^10,d^a=d^10,e^a=e^42,c^b=c^7d^2,d^b=c^10d^3

Conjugacy classes & character table

929 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31218, 21);