Finite Group Databasebeta

C32×#4837 #13162265

order1728
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productC32×#4837

Splittings

FittingC33×C4⋊C8 ⋊ C2
SylowC33 ⋊ #423

Subgroups

subgroupG/H
centerC2×C32×C4C22×D3
commutatorC22×C3C22×C32×C4
FrattiniC2×C4C22×C32×D3
FittingC33×C4⋊C8C2
socleC22×C33C22×C4
prime radicalC22×C32×D3C2×C4
cosocleC2×C3×C4C23×C32
hypercenterC32×C4⋊C8D3
hypocenterC3C32×#423
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C32×C4 ◁ C32×C4⋊C8

908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

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(1728, 28328);