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C9×#11923956 #23782790

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

Aliases

direct productC9×#11923956

Splittings

FittingC92×C43 ⋊ C3
SylowC43 ⋊ C9×3−1+2

Subgroups

subgroupG/H
centerC3×C9C3×C43⋊C3
commutatorC3×C43C32×C9
FrattiniC32C32×C43⋊C3
FittingC92×C43C3
socle, cosocleC32×C43C33
prime radicalC32×C43⋊C3C32
hypercenterC92C43⋊C3
hypocenterC43C9×3−1+2
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C3×C9 ◁ C92

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#11923956⋊C27, C27×#11923956, #44533603, …
maximal normal subgroup of#11923956⋊C27, C27×#11923956, #44533603, …
maximal quotient ofC9×(C3×C43⋊C3)⋊C9, C9×#16812500, C9×(C43⋊C9)⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 174);