Finite Group Databasebeta

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C2×C3×#11722576 #72245245

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

Aliases

direct productC2×C3×#11722576

Splittings

SylowC2×H(5,𝔽2) ⋊ C3×3−1+2

Subgroups

subgroupG/H
center, socleC22×C32C22×C3×A4
commutator, cosocleC3×Q8C23×C33
FrattiniC2×C3C23×C32×A4
Fitting, prime radicalC2×C33×H(5,𝔽2)C3
hypercenterC2×C33×Q8A4
hypocenterQ8C23×C3×3−1+2
LCSG ▷ C3×Q8 ▷ Q8
UCSC1 ◁ C22×C32 ◁ C2×C33×Q8

5194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#72245041, C2×#72252958
maximal normal subgroup ofC2×#72245041, C2×#72252958

GAP

Past the SmallGroups library coverage — no SmallGroups id.