C₅×C₁₇×D₂₁ #16813185

order	3570
isoclinism	isoclinic class of D₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₇×D₂₁
unambiguous semidirect product	C₃⋊(C₅×D₇×C₁₇)
unambiguous semidirect product	C₇⋊(C₅×D₃×C₁₇)

	subgroup	G/H
center, hypercenter	C₅×C₁₇	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₁₇

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 1785

A minimal faithful permutation representation — 2 generators on 32 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)(26,27,28,29,30,31,32);(24,25)(27,32)(28,31)(29,30)

1020 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3570, 12);