Finite Group Databasebeta

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C2×#13104837 #72223540

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C5

Aliases

direct productC2×#13104837

Splittings

FittingC2×C52×C22⋊C4 ⋊ C4
SylowC52 ⋊ C2×#385

Subgroups

subgroupG/H
centerC23C22×#1044
commutatorC22×C52C23×C4
FrattiniC22C23×#1044
FittingC2×C52×C22⋊C4C4
socleC23×C52C22×C4
prime radicalC24×C5⋊D5C22
cosocleC22×C5⋊D5C24
hypercenterC2×C22⋊C4#1044
hypocenterC52C2×#385
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C2×C22⋊C4

3138 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal quotient of#72223541

GAP

Past the SmallGroups library coverage — no SmallGroups id.