C₅×C₇×D₁₇ #11924731

order	1190
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₇×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₅×C₇)

	subgroup	G/H
center, hypercenter	C₅×C₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₅×C₇

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 595

A minimal faithful permutation representation — 2 generators on 29 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);(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1190, 1);