Finite Group Databasebeta

C4×C9×#208 #13142373

order1728
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C42×C9 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×C9×#208

Splittings

SylowC3×C9 ⋊ C4×M16

Subgroups

subgroupG/H
centerC42×C9C2×D3
commutatorC2×C3C2×C42×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C3×C42×C9C2
socleC22×C32C22×C3×C4
prime radicalC23×C32C2×C3×C4
cosocleC2×C32×C4C23×C3
hypercenterC2×C42×C9D3
hypocenterC3C4×C9×M16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C42×C9 ◁ C2×C42×C9

534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8436);