Finite Group Databasebeta

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C2×#10624901⋊C2 #72244105

order2916
automorphism?
homologyAbelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×#10624901⋊C2

Splittings

FittingC2×#10624901 ⋊ C2
Sylow#10624901 ⋊ C22

Subgroups

subgroupG/H
centerC2×C3C32×AGL(1,ℤ/9)
commutator, cosocleC3×C9C22×C33
FrattiniC32C2×C33×D3
FittingC2×#10624901C2
socleC2×C32C33×D3
prime radicalC2×D9⋊H(3,𝔽3)C3
hypercenterC2×3−1+2AGL(1,ℤ/9)
hypocenterC9C22×#737
LCSG ▷ C3×C9 ▷ C9
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

755 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221845
maximal quotient ofC2×#72221846

GAP

Past the SmallGroups library coverage — no SmallGroups id.