C₇×D₅×C₃₁ #14524243

order	2170
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₅×C₃₁
unambiguous semidirect product	C₅⋊(C₂×C₇×C₃₁)

	subgroup	G/H
center, hypercenter	C₇×C₃₁	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₃₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₇×C₃₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1085

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(9,12)(10,11)

868 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2170, 6);