Finite Group Databasebeta

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3−1+2×#1020 #72220101

order2592
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C23

Aliases

direct product3−1+2×#1020

Splittings

FittingC24×3−1+2 ⋊ D3

Subgroups

subgroupG/H
center, FrattiniC3C32×#1020
commutator, cosocleC3×C22⋊A4C2×C32
FittingC24×3−1+2D3
socleC24×C3C32×D3
prime radicalC32×#1020C3
hypercenter3−1+2#1020
hypocenterC22⋊A4C2×3−1+2
LCSG ▷ C3×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C3 ◁ 3−1+2

525 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 525 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#1020, 3−1+2×A4⋊S4
maximal normal subgroup ofAGL(1,ℤ/9)×#1020
maximal quotient of3−1+2×#5935, 3−1+2×#5934, 3−1+2×#5933

GAP

Past the SmallGroups library coverage — no SmallGroups id.