Finite Group Databasebeta

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C2×D32×#100 #72269115

order2304
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×D32×#100

Splittings

FittingC2×C32×#100 ⋊ C22
SylowC32 ⋊ C23×#100

Subgroups

subgroupG/H
centerC22D32×C22⋊C4
commutatorC22×C32C24×C4
FrattiniC2×C4C23×D32
FittingC2×C32×#100C22
socleC22×C32C22×C22⋊C4
prime radicalC22×D32×D4C2
cosocleC2×C32×C4C25
hypercenterC2×#100D32
hypocenterC32C23×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

14764 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.