C₂×#401⋊C₃ #73188

order	384
isoclinism	isoclinic class of #396⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×#401⋊C₃
unambiguous semidirect product	(C₂×#401)⋊C₃

	subgroup	G/H
center, hypercenter	C₂²	#126⋊C₃
commutator, cosocle, hypocenter	#95	C₂²×C₃
Frattini	C₂³	C₂²×A₄
Fitting	C₂×#401	C₃
socle	C₂⁴	C₂×A₄
prime radical	C₂×#95⋊C₃	C₂
LCS	G ▷ #95
UCS	C₁ ◁ C₂²

121 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)(3,9,21,11,5,17,8,18,12,4,14,25)(6,19,20,15,13,24,7,23,22,10,16,26);(1,2)(4,11)(5,16,14,13)(6,7)(9,19,18,23)(12,20)(17,26)(21,22)(24,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5764);