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H(5,𝔽₂)×C₂²⋊C₉ #11919875

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₉ · Schur multiplier (H₂) = C₂⁶

Aliases

H(5,𝔽₂)×C₂²⋊C₉

Splittings

C₂²×H(5,𝔽₂) ⋊ C₉

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₃	C₂⁴×A₄
commutator	C₂³	C₂⁴×C₉
Fitting, prime radical	C₂²×C₃×H(5,𝔽₂)	C₃
socle, cosocle	C₂³×C₃	C₂⁴×C₃
hypercenter	C₃×H(5,𝔽₂)	A₄
hypocenter	C₂²	C₉×H(5,𝔽₂)
LCS	G ▷ C₂³ ▷ C₂²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×H(5,𝔽₂)

2574 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 2574 conjugacy classes of subgroups — too many to draw. Only its 340 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 72

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153886);