Finite Group Databasebeta

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C2×#72224608 #72230727

order7200
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#72224608

Splittings

HallC32×C52 ⋊ C2×C22⋊C4
SylowC52 ⋊ C2×(C2×D3)⋊Dic3
SylowC32 ⋊ C2×#87831

Subgroups

subgroupG/H
center, hypercenterC22#14268439
commutatorC2×C32×C52C22×C4
FrattiniC2C2×#14268439
Fitting, socleC22×C32×C52C2×C4
prime radicalC22×C3×D15⋊D5C2
cosocleC2×C32×C5⋊D5C23
hypocenterC32×C52C2×C22⋊C4
LCSG ▷ C2×C32×C52 ▷ C32×C52
UCSC1 ◁ C22

1488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72224630
maximal normal subgroup ofC2×#72224630

GAP

Past the SmallGroups library coverage — no SmallGroups id.