Finite Group Databasebeta

C2×#13091566 #72244012

order2916
automorphism?
homologyAbelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×#13091566

Splittings

FittingC2×#10624918 ⋊ C2
Sylow#10624918 ⋊ C22

Subgroups

subgroupG/H
centerC2×C9C32×C3⋊D3
commutator, hypocenterH(3,𝔽3)C22×C3×C9
FrattiniC9C2×C32×C3⋊D3
FittingC2×#10624918C2
socleC2×C3C3×C9×C3⋊D3
prime radicalC2×C3×#272C9
cosocle#737C22×C32
hypercenterC2×C27⋊C3C3⋊D3
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C2×C9 ◁ C2×C27⋊C3

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#72221829, C2×#72221831, C2×#72221848
maximal normal subgroup ofC2×#72221831, C2×#72221848

GAP

Past the SmallGroups library coverage — no SmallGroups id.