C₂×C₃⋊(#395⋊C₃) #11921363

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×C₃⋊(#395⋊C₃)
unambiguous semidirect product	(C₂×C₃)⋊(#395⋊C₃)
unambiguous semidirect product	(C₂×#5230)⋊C₃

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊(#120⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₃×Q₈	C₂²×C₃
Frattini	C₂³	C₂×D₃×A₄
Fitting	C₂³×C₃×Q₈	C₂×C₃
socle	C₂⁴×C₃	C₂×A₄
prime radical	C₂×C₃×C₂²⋊SL(2,𝔽₃)	C₂
LCS	G ▷ C₂²×C₃×Q₈
UCS	C₁ ◁ C₂²

406 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 144

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 155374);