Finite Group Databasebeta

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C22×#11757845 #72244704

order3888
automorphism?
homologyAbelianization (H1) = C22×C33 · Schur multiplier (H2) = C22×C3

Aliases

direct productC22×#11757845

Splittings

SylowC24 ⋊ #6900

Subgroups

subgroupG/H
centerC22×C32C32×A4
commutator, cosocleC22×C32C22×C33
FrattiniC32C22×C32×A4
FittingC24×C3×3−1+2C3
socleC24×C32C33
prime radicalC24×C33C32
hypercenterC22×C3×3−1+2A4
hypocenterC22C22×#6900
LCSG ▷ C22×C32 ▷ C22
UCSC1 ◁ C22×C32 ◁ C22×C3×3−1+2

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 324

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22×#72220143, C22×#14518082
maximal normal subgroup ofC22×#14518082
maximal quotient ofC22×#72220143

GAP

Past the SmallGroups library coverage — no SmallGroups id.