D₇×C₁₉×C₅⋊D₅ #27210908

order	13300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	D₇×C₁₉×C₅⋊D₅
unambiguous semidirect product	(C₅×D₇)⋊(D₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₇×C₅⋊D₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂²
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₁₉

160 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 3325

A minimal faithful permutation representation — 3 generators on 36 points:

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

1330 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 66);