Finite Group Databasebeta

C3×C8×#208 #11773533

order1152
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×C8×#208

Splittings

SylowC32 ⋊ C8×M16

Subgroups

subgroupG/H
centerC3×C4×C8C2×D3
commutatorC2×C3C2×C3×C4×C8
FrattiniC42C22×C3×D3
FittingC2×C32×C4×C8C2
socleC22×C32C2×C42
prime radicalC23×C32C42
cosocleC3×C42C23×C3
hypercenterC2×C3×C4×C8D3
hypocenterC3C3×C8×M16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4×C8 ◁ C2×C3×C4×C8

529 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 7544);