Finite Group Databasebeta

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C3×#11724611 #72220355

order2592
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3

Aliases

direct productC3×#11724611

Splittings

FittingC23×C34 ⋊ C22
SylowC34 ⋊ H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C3C22×D3×C3⋊D3
commutator, cosocleC2×C33C24×C3
FrattiniC2C22×C3×D3×C3⋊D3
FittingC23×C34C22
socleC2×C34C24
hypercenterC23×C3D3×C3⋊D3
hypocenterC33C3×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C3 ◁ C23×C3

3466 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.