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C2×D31⋊C9 #11764348

order1116
isoclinismisoclinic class of D31⋊C3
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D31⋊C9
unambiguous semidirect productD31⋊(C2×C9)
unambiguous semidirect product(C2×D31)⋊C9
unambiguous semidirect product(C31⋊C9)⋊C22
unambiguous semidirect product(C2×C31⋊C9)⋊C2

Splittings

derived, SylowC31 ⋊ C22×C9
HallC31⋊C9 ⋊ C22
HallC2×D31 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC2×C3D31⋊C3
commutator, hypocenterC31C22×C9
FrattiniC3C2×D31⋊C3
Fitting, socleC2×C3×C31C2×C3
prime radicalC2×C3×D31C3
cosocleC3×C31C22×C3
LCSG ▷ C31
UCSC1 ◁ C2×C3

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 558

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×D31⋊C9, C2×C11×D31⋊C9, C2×C11⋊(D31⋊C9), …
maximal normal subgroup ofC2×C11×D31⋊C9, C2×C13×D31⋊C9, C2×C17×D31⋊C9, …
maximal quotient ofD11×D31⋊C9, C2×C11×D31⋊C9, C2×C11⋊(D31⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1116, 7);