Finite Group Databasebeta

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C2×#100×C5⋊D5 #72221219

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C5

Aliases

direct productC2×#100×C5⋊D5

Splittings

FittingC2×C52×#100 ⋊ C2
SylowC52 ⋊ C22×#100

Subgroups

subgroupG/H
centerC22C22⋊C4×C5⋊D5
commutatorC22×C52C23×C4
FrattiniC2×C4C23×C5⋊D5
FittingC2×C52×#100C2
socleC22×C52C2×C22⋊C4
prime radicalC22×D4×C5⋊D5C2
cosocleC2×C4×C52C24
hypercenterC2×#100C5⋊D5
hypocenterC52C22×#100
LCSG ▷ C22×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

3968 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

308 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊D5×#453, C2×#72221215, C2×#100×#1043, …
maximal normal subgroup ofC2×C5⋊D5×#453, C2×#72221215, C2×#100×#1043, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.