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C3×3−1+2×C43⋊C3 #23782912

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

Aliases

direct productC3×3−1+2×C43⋊C3

Splittings

FittingC3×3−1+2×C43 ⋊ C3
SylowC43 ⋊ C32×3−1+2

Subgroups

subgroupG/H
centerC32C32×C43⋊C3
commutator, cosocleC3×C43C34
FrattiniC3C33×C43⋊C3
FittingC3×3−1+2×C43C3
socleC32×C43C33
prime radicalC33×C43⋊C3C3
hypercenterC3×3−1+2C43⋊C3
hypocenterC43C32×3−1+2
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C3×3−1+2

576 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC43⋊C3×#6857, C43⋊C3×#6858, C43⋊C3×#6860, …
maximal normal subgroup ofC43⋊C3×#6857, C43⋊C3×#6858, C43⋊C3×#6860, …
maximal quotient ofC3×C32⋊C9×C43⋊C3, C3×C9⋊C9×C43⋊C3, C9×3−1+2×C43⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 296);