#11920014

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂³	C₂×(C₂²⋊C₉)⋊C₂
commutator	C₂×Q₈⋊C₉	C₂×C₄
Frattini, socle, prime radical	C₂³×C₃	C₂×S₄
Fitting	C₂×C₃×C₄×Q₈	D₃
cosocle	C₂²×Q₈⋊C₉	C₂²
hypercenter	C₂²×C₄	(C₂²⋊C₉)⋊C₂
hypocenter	Q₈⋊C₉	C₄⋊C₄
LCS	G ▷ C₂×Q₈⋊C₉ ▷ Q₈⋊C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

281 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 281 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

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

μ_t(G) = 1152

Polycyclic presentation:

2^4,3^2,2^3|a^2=d,b^2=c,e^3=f,g^2=i,h^2=i,b^a=bd,e^a=e^2f^2,f^a=f^2,g^a=gh,h^a=hi,g^e=h,h^e=ghi,h^g=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154025);