Finite Group Databasebeta

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C5⋊D5×#496 #72220944

order3200
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4×C5

Aliases

direct productC5⋊D5×#496

Splittings

FittingC52×#496 ⋊ C2
SylowC52 ⋊ C2×#496

Subgroups

subgroupG/H
centerC22C2×D4×C5⋊D5
commutator, cosocleC2×C4×C52C24
FrattiniC2×C4C23×C5⋊D5
FittingC52×#496C2
socleC22×C52C22×D4
hypercenter#496C5⋊D5
hypocenterC52C2×#496
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42 ◁ #496

2672 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5⋊D5×#3151, #72221134, #496×#1043, …
maximal normal subgroup ofC5⋊D5×#3151, #72221134, #496×#1043, …
maximal quotient ofC5⋊D5×#1715, C5⋊D5×#1721

GAP

Past the SmallGroups library coverage — no SmallGroups id.