C₇×C₁₁×D₁₃ #14523003

order	2002
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₁×D₁₃
unambiguous semidirect product	C₁₃⋊(C₂×C₇×C₁₁)

	subgroup	G/H
center, hypercenter	C₇×C₁₁	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₇×C₁₁

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);(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2002, 2);