C₂³×D₁₁ #4350

order	176
isoclinism	isoclinic class of D₁₁
automorphism	Aut(G) order 147840
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂³×D₁₁
unambiguous semidirect product	C₁₁⋊C₂⁴
unambiguous semidirect product	(C₂×C₁₁)⋊C₂³

Fitting, socle	C₂³×C₁₁ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂⁴

	subgroup	G/H
center, hypercenter	C₂³	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂³×C₁₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂³

134 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 88

A minimal faithful permutation representation — 4 generators on 17 points:

(1,2)(3,4)(5,6)(8,9)(10,11)(12,13)(14,15)(16,17);(5,6)(7,8,10,12,14,16,17,15,13,11,9);(3,4);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 41);