C₂×C₈²⋊C₃ #68012

order	384
isoclinism	isoclinic class of C₈²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₈

Aliases

direct product	C₂×C₈²⋊C₃
unambiguous semidirect product	(C₂×C₈²)⋊C₃

Fitting, Sylow	C₂×C₈² ⋊ C₃
derived	C₈² ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₂	C₈²⋊C₃
commutator, cosocle, hypocenter	C₈²	C₂×C₃
Frattini	C₄²	C₂×A₄
Fitting	C₂×C₈²	C₃
socle	C₂³	C₄²⋊C₃
LCS	G ▷ C₈²
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 588);