Finite Group Databasebeta

← Prev (#72245120) Next (#72245122) →

C2×C3×#11722589 #72245121

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

Aliases

direct productC2×C3×#11722589

Splittings

SylowC2×H(5,𝔽2) ⋊ C3×3−1+2

Subgroups

subgroupG/H
center, socleC22×C32C3×C22⋊A4
commutator, cosocleC3×H(5,𝔽2)C2×C33
FrattiniC2×C3C2×C32×C22⋊A4
Fitting, prime radicalC2×C33×H(5,𝔽2)C3
hypercenterC22×C33C22⋊A4
hypocenterH(5,𝔽2)C2×C3×3−1+2
LCSG ▷ C3×H(5,𝔽2) ▷ H(5,𝔽2)
UCSC1 ◁ C22×C32 ◁ C22×C33

4936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#72245041, C2×#72252942
maximal normal subgroup ofC2×#72245041, C2×#72252942

GAP

Past the SmallGroups library coverage — no SmallGroups id.