C₃²×D₇×C₃₁ #16840913

order	3906
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₃₁ · Schur multiplier (H₂) = C₃

Aliases

C₃²×D₇×C₃₁

	subgroup	G/H
center, hypercenter	C₃²×C₃₁	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₃₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₃₁

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 1953

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3)(7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44);(4,5,6)(8,13)(9,12)(10,11)

1395 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3906, 63);