Finite Group Databasebeta

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3−1+2×2−1+4⋊C3 #72245165

order2592
automorphism?
homologyAbelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C32

Aliases

direct product3−1+2×2−1+4⋊C3

Splittings

Fitting3−1+2×2−1+4 ⋊ C3
Sylow2−1+4 ⋊ C3×3−1+2

Subgroups

subgroupG/H
center, Frattini, socleC2×C3C22×C32×A4
commutator, cosocleC3×Q8C22×C33
Fitting3−1+2×2−1+4C3
prime radicalC32×2−1+4⋊C3C3
hypercenterD4×3−1+2A4
hypocenterQ8C22×C3×3−1+2
LCSG ▷ C3×Q8 ▷ Q8
UCSC1 ◁ C2×C3 ◁ D4×3−1+2

654 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 202 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) = 144

Conjugacy classes & character table

209 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72245618, #72253122
maximal normal subgroup of#72253122

GAP

Past the SmallGroups library coverage — no SmallGroups id.