#27188201

order	12943
automorphism	?
homology	Abelianization (H₁) = C₇ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Sylow

C₄₃² ⋊ C₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₄₃²	C₇
LCS	G ▷ C₄₃²
UCS	C₁

14 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 86
transitive degree	μ_t(G) = 301

A minimal faithful permutation representation — 2 generators on 86 points:

(2,3,5,9,14,22,35)(4,7,11,18,29,40,6)(8,13,20,33,10,16,25)(12,17,27,38,21,32,43)(15,24,37,34,23,19,31)(26,36,28,39,30,41,42)(45,46,48,52,59,70,82)(47,50,56,66,53,61,73)(49,54,63,77,80,64,79)(51,58,69,71,83,55,60)(57,67,68,78,84,81,86)(62,75,85,72,65,74,76);(1,2,4,8,5,10,17,28,11,19,32,22,20,34,24,37,14,23,36,33,25,35,40,43,38,31,42,18,30,39,41,27,29,16,26,9,15,13,21,7,12,3,6)(44,45,47,51,52,60,72,84,66,80,85,59,71,54,64,77,82,79,86,58,69,48,53,62,76,63,78,50,57,68,81,75,73,83,67,46,49,55,65,61,74,70,56)

Polycyclic presentation:

7,43^2|b^a=b^41,c^a=c^35

Conjugacy classes & character table

271 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#39905636, #39905637, #39905639, …
maximal normal subgroup of	#39905636, #39905637, #39905639, …
maximal quotient of	C₂×#27188201

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12943, 6);