C₃²×C₅×D₁₇ #13095256

order	1530
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₅ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₅×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₃²×C₅)

	subgroup	G/H
center, hypercenter	C₃²×C₅	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃²×C₅

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 765

A minimal faithful permutation representation — 2 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1530, 9);