Finite Group Databasebeta

← Prev (#23748680) Next (#23748682) →

C2×C3×C17×C31⋊C3 #23748681

order9486
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C17×C31⋊C3
unambiguous semidirect product(C2×C31)⋊(C32×C17)
unambiguous semidirect product(C2×C3×C31)⋊(C3×C17)
unambiguous semidirect product(C2×C17×C31)⋊C32
unambiguous semidirect product(C2×C3×C17×C31)⋊C3

Splittings

Fitting, socleC2×C3×C17×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C32×C17
HallC2×C17×C31 ⋊ C32
HallC17×C31 ⋊ C2×C32
HallC2×C31 ⋊ C32×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17C31⋊C3
commutator, cosocle, hypocenterC31C2×C32×C17
FrattiniC1G
Fitting, socleC2×C3×C17×C31C3
LCSG ▷ C31
UCSC1 ◁ C2×C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C17×(C31⋊C3)⋊C4, C3×(C31⋊C3)⋊Dic17, C3×Dic17×C31⋊C3, …
maximal normal subgroup ofC3×C17×(C31⋊C3)⋊C4, C3×(C31⋊C3)⋊Dic17, C3×Dic17×C31⋊C3, …
maximal quotient ofC3×C4×C17×C31⋊C3, C22×C3×C17×C31⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9486, 21);