C₂²×C₃×D₁₇ #88006

order	408
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂²×C₃×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂³×C₃)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₂²×C₃)

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂²×C₃

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 204

A minimal faithful permutation representation — 3 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 43);