C₃²×C₁₁×D₇ #13063467

order	1386
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₁ · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₁₁×D₇

	subgroup	G/H
center, hypercenter	C₃²×C₁₁	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₁₁

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 693

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3)(7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24);(4,5,6)(19,24)(20,23)(21,22)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1386, 22);