C₁₁×C₁₃×D₇ #14523006

order	2002
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×C₁₃×D₇
unambiguous semidirect product	C₇⋊(C₂×C₁₁×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₁×C₁₃

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1001

A minimal faithful permutation representation — 2 generators on 31 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);(26,31)(27,30)(28,29)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2002, 5);