Finite Group Databasebeta

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C₂³×#87832 #72223313

order	3200
isoclinism	isoclinic class of #87831
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

Splittings

C₅² ⋊ C₂³×C₄⋊C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁴	D₅⋊AGL(1,𝔽₅)
commutator	C₂×C₅²	C₂⁴×C₄
Frattini	C₂	C₂³×D₅⋊AGL(1,𝔽₅)
Fitting, socle	C₂⁴×C₅²	C₂×C₄
prime radical	C₂⁴×C₅⋊D₅	C₂²
cosocle	C₂×C₅⋊D₅	C₂⁵
hypocenter	C₅²	C₂³×C₄⋊C₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂⁴

6338 conjugacy classes of subgroups; only the 1291 normal subgroups are shown.

normal subgroups only

This group has 6338 conjugacy classes of subgroups — too many to draw. Only its 1291 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal quotient of

GAP

Past the SmallGroups library coverage — no SmallGroups id.