Finite Group Databasebeta

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C22×C9×#1043 #72247284

order3600
automorphism?
homologyAbelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23

Aliases

direct productC22×C9×#1043

Splittings

FittingC22×C52×C9 ⋊ C4
derived, SylowC52 ⋊ C22×C4×C9
HallC52×C9 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22×C9#1043
commutator, hypocenterC52C22×C4×C9
FrattiniC3C22×C3×#1043
FittingC22×C52×C9C4
socleC22×C3×C52C3×C4
prime radicalC22×C3×C5⋊D5C2×C3
cosocleC3×C5⋊D5C23×C3
LCSG ▷ C52
UCSC1 ◁ C22×C9

648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 900

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22×D9×#1043, C22×3−1+2×#1043, C9×#11717375, …
maximal normal subgroup ofC22×D9×#1043, C22×3−1+2×#1043, C9×#11717375, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.