Finite Group Databasebeta

C23×#872 #11701745

order768
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC23×#872

Splittings

FittingC23×C3×C42 ⋊ C2
SylowC3 ⋊ C23×#117

Subgroups

subgroupG/H
centerC24×C4C2×D3
commutatorC2×C3C25×C4
FrattiniC22C25×D3
FittingC23×C3×C42C2
socleC25×C3C23
prime radicalC25×D3C22
cosocleC22×C3C26
hypercenterC23×C42D3
hypocenterC3C23×#117
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C4 ◁ C23×C42

14334 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(768, 1076126);