Finite Group Databasebeta

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3−1+2×#5935 #72220103

order5184
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C22

Aliases

direct product3−1+2×#5935

Splittings

Fitting3−1+2×H(5,𝔽2) ⋊ D3

Subgroups

subgroupG/H
center, Frattini, socleC2×C3C32×#1020
commutator, cosocleC3×#997C2×C32
Fitting3−1+2×H(5,𝔽2)D3
prime radicalC32×#5935C3
hypercenterC2×3−1+2#1020
hypocenter#997C2×3−1+2
LCSG ▷ C3×#997 ▷ #997
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

745 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 745 conjugacy classes of subgroups — too many to draw. Only its 56 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

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#5935
maximal normal subgroup ofAGL(1,ℤ/9)×#5935

GAP

Past the SmallGroups library coverage — no SmallGroups id.