C₂×#376⋊C₃ #73161

order	384
isoclinism	isoclinic class of #95⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×#376⋊C₃
unambiguous semidirect product	(C₂×#376)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₄	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₂²×C₃
Frattini	C₂³	C₂²×A₄
Fitting	C₂×#376	C₃
socle	C₂⁴	C₂×A₄
prime radical	C₂×#95⋊C₃	C₂
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₄

175 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5737);