Finite Group Databasebeta

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C2×3−1+2×#997 #72245854

order5184
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C23×C32

Aliases

direct productC2×3−1+2×#997

Splittings

FittingC2×3−1+2×H(5,𝔽2) ⋊ C3
SylowC2×H(5,𝔽2) ⋊ C3×3−1+2

Subgroups

subgroupG/H
center, socleC22×C3C32×C22⋊A4
commutator, cosocleC3×H(5,𝔽2)C2×C33
FrattiniC2×C3C2×C32×C22⋊A4
FittingC2×3−1+2×H(5,𝔽2)C3
prime radicalC2×C32×#997C3
hypercenterC22×3−1+2C22⋊A4
hypocenterH(5,𝔽2)C2×C3×3−1+2
LCSG ▷ C3×H(5,𝔽2) ▷ H(5,𝔽2)
UCSC1 ◁ C22×C3 ◁ C22×3−1+2

2116 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 2116 conjugacy classes of subgroups — too many to draw. Only its 169 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

242 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,ℤ/9)×#997
maximal normal subgroup ofC2×AGL(1,ℤ/9)×#997

GAP

Past the SmallGroups library coverage — no SmallGroups id.