Finite Group Databasebeta

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C2×C22⋊C4×#1044 #72223524

order3200
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4×C5

Aliases

direct productC2×C22⋊C4×#1044

Splittings

FittingC2×C52×C22⋊C4 ⋊ C4
SylowC52 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23C22×#1044
commutatorC2×C52C22×C42
FrattiniC22C23×#1044
FittingC2×C52×C22⋊C4C4
socleC23×C52C22×C4
prime radicalC24×C5⋊D5C22
cosocleC22×C5⋊D5C24
hypercenterC2×C22⋊C4#1044
hypocenterC52C2×C4×C22⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C2×C22⋊C4

3394 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal quotient of#72223525

GAP

Past the SmallGroups library coverage — no SmallGroups id.