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C32×#11923956 #23782913

order10449
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC32×#11923956

Splittings

FittingC32×C9×C43 ⋊ C3
SylowC43 ⋊ C32×3−1+2

Subgroups

subgroupG/H
centerC33C3×C43⋊C3
commutator, cosocleC3×C43C34
FrattiniC3C33×C43⋊C3
FittingC32×C9×C43C3
socleC33×C43C32
prime radicalC33×C43⋊C3C3
hypercenterC32×C9C43⋊C3
hypocenterC43C32×3−1+2
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C33 ◁ C32×C9

576 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#44532107, #44532291, #44532310, …
maximal normal subgroup of#44532107, #44532291, #44532310, …
maximal quotient ofC32×(C3×C43⋊C3)⋊C9, C32×(C43⋊C9)⋊C9, C32×#16812500, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 297);