Finite Group Databasebeta

C4×#64138 #11802139

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3

Aliases

direct productC4×#64138

Splittings

FittingC22×C32×C42 ⋊ C2
SylowC32 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×C3⋊D3
commutatorC22×C32C23×C4
FrattiniC23C23×C3⋊D3
FittingC22×C32×C42C2
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC22×C42C3⋊D3
hypocenterC32C4×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C42

2064 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, 36150);