Finite Group Databasebeta

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C2×#13104711 #72221350

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

Aliases

direct productC2×#13104711

Splittings

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

Subgroups

subgroupG/H
centerC23C22×#1043
commutatorC22×C52C23×C4
FrattiniC22C23×#1043
FittingC2×C52×C22⋊C4C4
socleC23×C52C22×C4
prime radicalC24×C5⋊D5C22
cosocleC22×C5⋊D5C24
hypercenterC2×C22⋊C4#1043
hypocenterC52C2×#385
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C2×C22⋊C4

4928 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72223257, C2×#120×#1043, #72258374
maximal normal subgroup of#72223257, C2×#120×#1043, #72258374
maximal quotient ofC2×#72221210, C2×#72221215

GAP

Past the SmallGroups library coverage — no SmallGroups id.