C₅×C₁₇×C₃⋊D₃ #13095263

order	1530
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₁₇×C₃⋊D₃
unambiguous semidirect product	C₃⋊(C₅×D₃×C₁₇)

	subgroup	G/H
center, hypercenter	C₅×C₁₇	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₇	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₁₇

48 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1530, 16);