Finite Group Databasebeta

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C4⋊C4×#611 #11805414

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×#611

Splittings

FittingC22×C9×C4⋊C4 ⋊ C2
SylowC9 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC22×C9×C4⋊C4C2
prime radicalC22×#611C22
cosocleC23×C9C24
hypercenterC22×C4⋊C4D9
hypocenterC9D4×C4⋊C4
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4⋊C4

1164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 39425);