Finite Group Databasebeta

C8×#3828 #11861539

order1152
isoclinismisoclinic class of #634
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C3

Aliases

direct productC8×#3828

Splittings

FittingC2×C32×C4×C8 ⋊ C2
SylowC32 ⋊ C8×#41

Subgroups

subgroupG/H
centerC4×C8C2×C3⋊D3
commutatorC2×C32C23×C8
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4×C8C2
socleC22×C32C23×C4
prime radicalC2×#3828C4
cosocleC2×C32×C4C24
hypercenterC2×C4×C8C3⋊D3
hypocenterC32C8×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

1368 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, 95550);