Finite Group Databasebeta

← Prev (#11800757) Next (#11800759) →

C4×#64101 #11800758

order1152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C3×C42

Aliases

direct productC4×#64101

Splittings

FittingC32×C4×C4⋊C4 ⋊ C2
SylowC32 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×C3⋊D3
commutatorC2×C32C22×C42
FrattiniC23C23×C3⋊D3
FittingC32×C4×C4⋊C4C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

2256 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, 34769);