Finite Group Databasebeta

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C3×(C3×C43⋊C3)⋊C9 #23782773

order10449
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productC3×(C3×C43⋊C3)⋊C9

Splittings

FittingC32×C9×C43 ⋊ C3
SylowC43 ⋊ C3×C32⋊C9

Subgroups

subgroupG/H
centerC33C3×C43⋊C3
commutatorC3×C43C32×C9
FrattiniC32C32×C43⋊C3
FittingC32×C9×C43C3
socleC33×C43C32
prime radicalC33×C43⋊C3C3
cosocleC32×C43C33
hypercenterC32×C9C43⋊C3
hypocenterC43C3×C32⋊C9
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C33 ◁ C32×C9

288 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#44532236, C9×(C3×C43⋊C3)⋊C9, #44532245, …
maximal normal subgroup of#44532236, C9×(C3×C43⋊C3)⋊C9, #44532245, …
maximal quotient ofC3×C43⋊#6855, C9×(C3×C43⋊C3)⋊C9, #44532245, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 157);