C₅×D₇×C₁₉ #13050595

order	1330
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₇×C₁₉
unambiguous semidirect product	C₇⋊(C₂×C₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₁₉

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 665

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);(7,12)(8,11)(9,10)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1330, 2);