Finite Group Databasebeta

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C2×#72221859 #72244157

order5832
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C23

Aliases

direct productC2×#72221859

Splittings

FittingC2×C32×C9⋊C9 ⋊ C22
derivedC32×C9 ⋊ C23×C9
SylowC32×C9⋊C9 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC2×C3#66431⋊C3
commutator, hypocenterC32×C9C23×C9
FrattiniC32C2×C3×#1113
FittingC2×C32×C9⋊C9C22
socleC2×C34C2×C3×D3
prime radicalC2×C3×#66431C3
cosocleC33×C9C23×C3
LCSG ▷ C32×C9
UCSC1 ◁ C2×C3

1317 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#72221862, C2×#72221868, C2×#72221872
maximal quotient ofC2×#72221860

GAP

Past the SmallGroups library coverage — no SmallGroups id.