Finite Group Databasebeta

C3×D3×C8×Q8 #11861245

order1152
automorphism?
homologyAbelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C25

Aliases

direct productC3×D3×C8×Q8

Splittings

FittingC32×C8×Q8 ⋊ C2
SylowC32 ⋊ C2×C8×Q8

Subgroups

subgroupG/H
centerC2×C3×C8C22×D3
commutatorC2×C3C23×C3×C8
FrattiniC2×C4C23×C3×D3
FittingC32×C8×Q8C2
socleC22×C32C23×C4
prime radicalC22×C3×D3C22×C4
cosocleC2×C3×C4C24×C3
hypercenterC3×C8×Q8D3
hypocenterC3C2×C3×C8×Q8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C3×C8×Q8

931 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 95256);