Finite Group Databasebeta

C2×C4×#3663 #11857136

order1152
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#3663

Splittings

FittingC2×C4×C8×C9 ⋊ C2
SylowC9 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C42C2×D9
commutatorC2×C9C22×C42
FrattiniC2×C3×C4C23×D3
FittingC2×C4×C8×C9C2
socleC23×C3C2×C4×D3
prime radicalC23×D9C2×C4
cosocleC2×C4×C9C24
hypercenterC2×C4×C8D9
hypocenterC9C2×C4×M16
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

984 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, 91147);