C₇×C₁₃×D₁₁ #14523004

order	2002
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₃×D₁₁
unambiguous semidirect product	C₁₁⋊(C₂×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₇×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);(22,31)(23,30)(24,29)(25,28)(26,27)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2002, 3);