Finite Group Databasebeta

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C2×D3×#1313 #72245702

order1536
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D3×#1313

Splittings

FittingC2×C3×#1313 ⋊ C2
SylowC3 ⋊ C22×#1313

Subgroups

subgroupG/H
centerC22×C4C42×D3
commutatorC3×C4C22×C4×C8
FrattiniC4×C8C23×D3
FittingC2×C3×#1313C2
socleC23×C3C2×#97
prime radicalC23×D3#97
cosocleC3×C4×C8C24
hypercenterC2×#1313D3
hypocenterC3C22×#1313
LCSG ▷ C3×C4 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#1313

1444 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 768

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D3×#12067, C2×D3×#7333, C2×C3⋊D3×#1313, …
maximal normal subgroup ofC2×D3×#12067, C2×D3×#7333, C2×D3×#12068
maximal quotient ofC2×D3×#7333, C2×C3⋊D3×#1313

GAP

Past the SmallGroups library coverage — no SmallGroups id.