#27188200

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)(45,46,48,52,59,71,83)(47,50,56,66,79,84,60)(49,54,63,76,67,51,58)(53,61,73,70,57,68,81)(55,64,69,82,86,77,72)(62,75,85,80,65,78,74);(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)(44,45,47,51,46,49,55,65,50,57,69,83,58,70,73,81,48,53,62,76,54,52,60,72,64,61,74,84,78,75,85,86,56,67,80,71,68,63,77,79,82,59,66)

Polycyclic presentation:

7,43^2|b^a=b^41,c^a=c^4

Conjugacy classes & character table

271 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#39905634, #39905635, #39905638, …
maximal normal subgroup of	#39905634, #39905635, #39905638, …
maximal quotient of	C₂×#27188200

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12943, 5);