Finite Group Databasebeta

C4×#64081 #11800764

order1152
isoclinismisoclinic class of #634
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C3×C42

Aliases

direct productC4×#64081

Splittings

FittingC32×C43 ⋊ C2
SylowC32 ⋊ C4×#117

Subgroups

subgroupG/H
centerC2×C42C2×C3⋊D3
commutatorC2×C32C22×C42
FrattiniC23C23×C3⋊D3
FittingC32×C43C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC43C3⋊D3
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C42 ◁ C43

2256 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 34775);