Finite Group Databasebeta

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C4×#10591522 #72259921

order2304
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#10591522

Splittings

FittingC2×C32×C4×D4 ⋊ C22
SylowC32 ⋊ C4×#453

Subgroups

subgroupG/H
centerC2×C4#63983
commutatorC2×C32×C4C23×C4
FrattiniC22×C4C22×D32
FittingC2×C32×C4×D4C22
socleC22×C32C2×#120
prime radicalC2×#10591522C2
cosocleC22×C32×C4C24
hypercenterC2×C4×D4D32
hypocenterC32C4×#453
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

3618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#11864777
maximal normal subgroup ofC4×#11864777

GAP

Past the SmallGroups library coverage — no SmallGroups id.