Finite Group Databasebeta

C4×#63464 #11857247

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

Aliases

direct productC4×#63464

Splittings

FittingC2×C4×C8×C9 ⋊ C2
SylowC9 ⋊ C4×#131

Subgroups

subgroupG/H
centerC4×C8C2×D9
commutatorC2×C9C22×C42
FrattiniC2×C3×C4C23×D3
FittingC2×C4×C8×C9C2
socleC22×C3C22×C4×D3
prime radicalC2×#3697C22
cosocleC2×C4×C9C24
hypercenterC2×C4×C8D9
hypocenterC9C4×#131
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

858 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, 91258);