Finite Group Databasebeta

C3×#67808 #11772384

order1152
isoclinismisoclinic class of D48
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC3×#67808

Splittings

SylowC32 ⋊ #1381

Subgroups

subgroupG/H
centerC2×C3×C4D24
commutatorC3×C8C3×C42
FrattiniC22×C8C2×C3×D3
FittingC22×C32×C16C2
socleC22×C32#107
prime radicalC23×C32Q16
cosocleC22×C3×C8C22×C3
hypercenterC22×C3×C16D3
hypocenterC3C3×#1381
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C22×C3×C16

305 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 6395);