Finite Group Databasebeta

C3×C8×#611 #13143093

order1728
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productC3×C8×#611

Splittings

FittingC22×C3×C8×C9 ⋊ C2
SylowC3×C9 ⋊ C8×D4

Subgroups

subgroupG/H
centerC2×C3×C8C2×D9
commutatorC2×C9C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC22×C3×C8×C9C2
socleC22×C32C2×C4×D3
prime radicalC2×C3×#611C4
cosocleC2×C4×C9C23×C3
hypercenterC22×C3×C8D9
hypocenterC9C3×C8×D4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3×C8 ◁ C22×C3×C8

478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 9156);