Finite Group Databasebeta

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C5⋊D5×#453 #72221207

order3200
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26×C5

Aliases

direct productC5⋊D5×#453

Splittings

FittingC52×#453 ⋊ C2
SylowC52 ⋊ C2×#453

Subgroups

subgroupG/H
centerC2#120×C5⋊D5
commutator, cosocleC2×C4×C52C24
FrattiniC2×C4C23×C5⋊D5
FittingC52×#453C2
socleC2×C52C2×#120
hypercenter#453C5⋊D5
hypocenterC52C2×#453
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

3376 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#453×#1043, C2×C5⋊D5×#453, #72223390, …
maximal normal subgroup of#453×#1043, C2×C5⋊D5×#453, #72223390, …
maximal quotient ofC2×C5⋊D5×#453

GAP

Past the SmallGroups library coverage — no SmallGroups id.