Finite Group Databasebeta

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C4×#63454 #11800757

order1152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#63454

Splittings

FittingC4×C9×C4⋊C4 ⋊ C2
SylowC9 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D9
commutatorC2×C9C22×C42
Frattini, socleC23×C3C23×D3
FittingC4×C9×C4⋊C4C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenterC4×C4⋊C4D9
hypocenterC9C4×#117
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

1128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 34768);