Finite Group Databasebeta

C2×C32×#907 #13179121

order1728
automorphism?
homologyAbelianization (H1) = C23×C32×C4 · Schur multiplier (H2) = C25×C3

Aliases

direct productC2×C32×#907

Splittings

FittingC2×C33×M16 ⋊ C2
SylowC33 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C32×C4C22×D3
commutatorC2×C3C23×C32×C4
FrattiniC4C23×C32×D3
FittingC2×C33×M16C2
socleC22×C33C22×C4
prime radicalC2×C32×#235C2
cosocleC3×C4C24×C32
hypercenterC2×C32×M16D3
hypocenterC3C2×C32×#131
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C32×C4 ◁ C2×C32×M16

1868 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 45184);