Finite Group Databasebeta

C9×#63499 #72220009

order2592
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C24

Aliases

direct productC9×#63499

Splittings

FittingC2×D4×C92 ⋊ C2
SylowC92 ⋊ #120

Subgroups

subgroupG/H
centerC22×C9C22×D9
commutatorC22×C9C23×C9
Frattini, socleC22×C32C22×C3×D3
FittingC2×D4×C92C2
prime radicalC3×#63499C3
cosocleC22×C3×C9C23×C3
hypercenterC2×D4×C9D9
hypocenterC9C9×#120
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C9 ◁ C2×D4×C9

774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72220021, #72220068
maximal normal subgroup of#72220021, #72220068
maximal quotient ofC9×#10588757, C9×#10588712

GAP

Past the SmallGroups library coverage — no SmallGroups id.