Finite Group Databasebeta

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#453×#1035 #72275705

order6400
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#453×#1035

Splittings

FittingC25×#453 ⋊ C4
SylowC25 ⋊ C4×#453

Subgroups

subgroupG/H
centerC2#120×#1035
commutatorC2×C4×C25C23×C4
FrattiniC2×C4×C5C23×AGL(1,𝔽5)
FittingC25×#453C4
socleC2×C5AGL(1,𝔽5)×#120
prime radicalD25×#453C2
cosocleC2×C4×D25C24
hypercenter#453#1035
hypocenterC25C4×#453
LCSG ▷ C2×C4×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

2367 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.