Finite Group Databasebeta

C22×C3×#809 #11857717

order1152
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×C3×#809

Splittings

FittingC22×C32×C4⋊C4 ⋊ C2
SylowC32 ⋊ C22×#102

Subgroups

subgroupG/H
centerC24×C3#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC22×C32×C4⋊C4C2
socleC24×C32D4
prime radicalC23×C3×D12C2
cosocleC2×C3×C4C24×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C22×C3×#102
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C23×C3×C4 ◁ C22×C3×C4⋊C4

2353 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 91728);