Finite Group Databasebeta

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3−1+2×#1094 #72276214

order2916
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C2×C34

Aliases

direct product3−1+2×#1094

Splittings

SylowC22 ⋊ 3−1+22

Subgroups

subgroupG/H
center, FrattiniC32C33×A4
commutator, socle, cosocleC22×C32C34
FittingC22×C32×3−1+2C3
prime radicalC22×C34C32
hypercenterC32×3−1+2A4
hypocenterC223−1+22
LCSG ▷ C22×C32 ▷ C22
UCSC1 ◁ C32 ◁ C32×3−1+2

1124 conjugacy classes of subgroups; only the 316 normal subgroups are shown.

normal subgroups only

This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 316 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10942
maximal quotient of#10942

GAP

Past the SmallGroups library coverage — no SmallGroups id.