#11923767

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂³×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂	C₂×C₃⋊#1020
commutator, prime radical, cosocle	C₂×C₃×C₂²⋊A₄	C₂²
Fitting	C₂⁴×C₃×C₄	D₃
socle	C₂⁵×C₃	C₂×D₃
hypercenter	C₄	C₃⋊#1020
hypocenter	C₃×C₂²⋊A₄	Q₈
LCS	G ▷ C₂×C₃×C₂²⋊A₄ ▷ C₃×C₂²⋊A₄
UCS	C₁ ◁ C₂ ◁ C₄

760 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

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

μ_t(G) = 72

Polycyclic presentation:

2^3,3^2,2^4|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^2,f^a=fg,h^a=hi,f^d=g,g^d=fg,h^d=i,i^d=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 157778);