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C3×3−1+2×C31⋊C3 #21419426

order7533
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC3×3−1+2×C31⋊C3

Splittings

FittingC3×3−1+2×C31 ⋊ C3
SylowC31 ⋊ C32×3−1+2

Subgroups

subgroupG/H
centerC32C32×C31⋊C3
commutatorC3×C31C34
FrattiniC3C33×C31⋊C3
FittingC3×3−1+2×C31C3
socleC32×C31C33
hypercenterC3×3−1+2C31⋊C3
hypocenterC31C32×3−1+2
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C32 ◁ C3×3−1+2

576 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

429 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC31⋊C3×#6857, C31⋊C3×#6858, C31⋊C3×#6860, …
maximal normal subgroup ofC31⋊C3×#6857, C31⋊C3×#6858, C31⋊C3×#6860, …
maximal quotient ofC3×C32⋊C9×C31⋊C3, C3×C9⋊C9×C31⋊C3, C9×3−1+2×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7533, 296);