Finite Group Databasebeta

← Prev (#72223469) Next (#72223471) →

C₂³×#87831 #72223470

order	3200
isoclinism	isoclinic class of #87831
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹¹

Aliases

Splittings

C₅² ⋊ C₂³×C₂²⋊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×D₅²	C₂
cosocle	C₂×C₅⋊D₅	C₂⁵
hypocenter	C₅²	C₂³×C₂²⋊C₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂⁴

10626 conjugacy classes of subgroups; only the 1291 normal subgroups are shown.

normal subgroups only

This group has 10626 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.