Finite Group Databasebeta

← Prev (#22578607) Next (#22578609) →

C3×C11×D133 #22578608

order8778
isoclinismisoclinic class of D133
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D133

Splittings

Fitting, socle, HallC3×C7×C11×C19 ⋊ C2
derived, HallC7×C19 ⋊ C2×C3×C11
HallC7×C11×C19 ⋊ C2×C3
HallC3×C11×C19 ⋊ D7
HallC3×C7×C19 ⋊ C2×C11
HallC3×C7×C11 ⋊ D19
HallC11×C19 ⋊ C3×D7
HallC7×C11 ⋊ C3×D19
HallC3×C19 ⋊ C11×D7
HallC3×C7 ⋊ C11×D19
SylowC19 ⋊ C3×C11×D7
SylowC7 ⋊ C3×C11×D19

Subgroups

subgroupG/H
center, hypercenterC3×C11D133
commutator, hypocenterC7×C19C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2
LCSG ▷ C7×C19
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×D7×D19, C3×D11×D133, C3×D77⋊D19, …
maximal normal subgroup ofC3×C11×D7×D19, C3×D11×D133, C3×D77⋊D19, …
maximal quotient ofC3×C11×Dic133, C2×C3×C11×D133, C9×C11×D133, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 10);