Finite Group Databasebeta

C23×C3×#208 #11918438

order1152
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×C3×#208

Splittings

SylowC32 ⋊ C23×M16

Subgroups

subgroupG/H
centerC23×C3×C4C2×D3
commutatorC2×C3C24×C3×C4
FrattiniC4C24×C3×D3
FittingC24×C32×C4C2
socleC24×C32C2×C4
prime radicalC25×C32C4
cosocleC3×C4C25×C3
hypercenterC24×C3×C4D3
hypocenterC3C23×C3×M16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3×C4 ◁ C24×C3×C4

4121 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, 152449);