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C31⋊C32 #22575713

order8649
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

direct productC31⋊C32
unambiguous semidirect product(C31×C31⋊C3)⋊C3
unambiguous semidirect product#15668332⋊C3
unambiguous semidirect product#15668333⋊C3

Splittings

Fitting, socle, derived, SylowC312 ⋊ C32

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC312C32
LCSG ▷ C312
UCSC1

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

169 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C31⋊C3)⋊(D31⋊C3), C31⋊C3×D31⋊C3, #19153449⋊C3, …
maximal normal subgroup of(C31⋊C3)⋊(D31⋊C3), C31⋊C3×D31⋊C3, #19153449⋊C3, …
maximal quotient ofC2×C31⋊C32, C31⋊C3×C22⋊(C31⋊C3), #15668332⋊A4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8649, 10);