Finite Group Databasebeta

C4×#63491 #11802138

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#63491

Splittings

FittingC22×C42×C9 ⋊ C2
SylowC9 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC22×C42×C9C2
prime radicalC22×#611C22
cosocleC23×C9C24
hypercenterC22×C42D9
hypocenterC9C4×#123
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C22×C42

1032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 36149);