Finite Group Databasebeta

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C2×C3×C11×C31⋊C3 #20259573

order6138
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C11×C31⋊C3
unambiguous semidirect product(C2×C31)⋊(C32×C11)
unambiguous semidirect product(C2×C3×C31)⋊(C3×C11)
unambiguous semidirect product(C2×C11×C31)⋊C32
unambiguous semidirect product(C2×C3×C11×C31)⋊C3

Splittings

Fitting, socleC2×C3×C11×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C32×C11
HallC2×C11×C31 ⋊ C32
HallC11×C31 ⋊ C2×C32
HallC2×C31 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C31⋊C3
commutator, hypocenterC31C2×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C31C3
LCSG ▷ C31
UCSC1 ◁ C2×C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

858 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×(C31⋊C3)⋊C4, C3×C11⋊((C31⋊C3)⋊C4), C3×Dic11×C31⋊C3, …
maximal normal subgroup ofC3×C11×(C31⋊C3)⋊C4, C3×C11⋊((C31⋊C3)⋊C4), C3×Dic11×C31⋊C3, …
maximal quotient ofC3×C4×C11×C31⋊C3, C22×C3×C11×C31⋊C3, C3×D5×C11×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6138, 21);