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C3×C23×C31⋊C3 #20264384

order6417
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C32×C23 · Schur multiplier (H2) = C3

Aliases

direct productC3×C23×C31⋊C3
unambiguous semidirect productC31⋊(C32×C23)
unambiguous semidirect product(C3×C31)⋊(C3×C23)
unambiguous semidirect product(C23×C31)⋊C32
unambiguous semidirect product(C3×C23×C31)⋊C3

Splittings

Fitting, socleC3×C23×C31 ⋊ C3
derived, SylowC31 ⋊ C32×C23
HallC23×C31 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C23C31⋊C3
commutator, hypocenterC31C32×C23
FrattiniC1G
Fitting, socleC3×C23×C31C3
LCSG ▷ C31
UCSC1 ◁ C3×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

897 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C23×D31⋊C3, C3×C23⋊(D31⋊C3), C3×D23×C31⋊C3, …
maximal normal subgroup ofC3×C23×D31⋊C3, C3×C23⋊(D31⋊C3), C3×D23×C31⋊C3, …
maximal quotient ofC2×C3×C23×C31⋊C3, A4×C23×C31⋊C3, C3×C23×C22⋊(C31⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6417, 4);