Finite Group Databasebeta

C2×C3×D3×#131 #11918451

order1152
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C3×D3×#131

Splittings

FittingC2×C32×#131 ⋊ C2
SylowC32 ⋊ C22×#131

Subgroups

subgroupG/H
centerC2×C3×C8C22×D3
commutatorC2×C3C24×C3×C4
FrattiniC4C24×C3×D3
FittingC2×C32×#131C2
socleC22×C32C23×C4
prime radicalC2×C3×D3×#41C2
cosocleC3×C4C25×C3
hypercenterC2×C3×#131D3
hypocenterC3C22×C3×#131
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C2×C3×#131

3141 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

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, 152462);