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C3×(C43⋊C9)⋊C9 #23782776

order10449
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC3×(C43⋊C9)⋊C9

Splittings

SylowC43 ⋊ C3×C9⋊C9

Subgroups

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

180 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#44532240, C9×(C43⋊C9)⋊C9, #44532248, …
maximal normal subgroup of#44532240, C9×(C43⋊C9)⋊C9, #44532248, …
maximal quotient ofC3×C43⋊#6855, C9×(C43⋊C9)⋊C9, #44532248, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 160);