C₁₁×D₁₇ #67325

order	374
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₁₁)

Fitting, socle, Hall	C₁₁×C₁₇ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₁₁

	subgroup	G/H
center, hypercenter	C₁₁	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₁₁

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 187

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(374, 2);