#11807986

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂³	C₂³×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini, socle, prime radical	C₂³×C₃	C₂³×D₃
Fitting	C₂×C₉×#125	C₂
cosocle	C₂³×C₉	C₂⁴
hypercenter	C₂×#125	D₉
hypocenter	C₉	#2382
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×#125

612 conjugacy classes of subgroups; only the 294 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 294 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:

2^7,3^2|a^2=g,b^2=f,c^2=f,d^2=e,h^3=i,b^a=be,c^a=cf,d^a=def,h^a=h^2i^2,i^a=i^2,c^b=cef,d^b=de

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 41997);