Finite Group Databasebeta

C4×#63434 #11800763

order1152
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#63434

Splittings

FittingC43×C9 ⋊ C2
SylowC9 ⋊ C4×#117

Subgroups

subgroupG/H
centerC2×C42C2×D9
commutatorC2×C9C22×C42
Frattini, socleC23×C3C23×D3
FittingC43×C9C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenterC43D9
hypocenterC9C4×#117
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C42 ◁ C43

1128 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, 34774);