Finite Group Databasebeta

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C9×#11923958 #23782788

order10449
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C32

Aliases

direct productC9×#11923958

Splittings

SylowC43 ⋊ C9×3−1+2

Subgroups

subgroupG/H
centerC3×C9C3×C43⋊C3
commutatorC3×C43C32×C9
FrattiniC32C32×C43⋊C3
FittingC32×C9×C43C3
socle, cosocleC32×C43C33
prime radicalC33×C43C32
hypercenterC32×C9C43⋊C3
hypocenterC43C9×3−1+2
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C3×C9 ◁ C32×C9

148 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1233 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#44531896, #44531898, #44531899, …
maximal normal subgroup of#44531896, #44531898, #44531899, …
maximal quotient ofC9×C32⋊(C43⋊C9), C9×(C43⋊C9)⋊C9, #44532279, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 172);