Finite Group Databasebeta

← Prev (#22575118) Next (#22575120) →

C22×C3×C13×C11⋊C5 #22575119

order8580
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC22×C3×C13×C11⋊C5
unambiguous semidirect product(C22×C3×C11)⋊(C5×C13)
unambiguous semidirect product(C22×C3×C11×C13)⋊C5

Splittings

Fitting, socle, HallC22×C3×C11×C13 ⋊ C5
derived, SylowC11 ⋊ C22×C3×C5×C13
HallC22×C11×C13 ⋊ C3×C5
HallC3×C11×C13 ⋊ C22×C5
HallC11×C13 ⋊ C22×C3×C5
HallC22×C3×C11 ⋊ C5×C13
HallC22×C11 ⋊ C3×C5×C13
HallC3×C11 ⋊ C22×C5×C13

Subgroups

subgroupG/H
center, hypercenterC22×C3×C13C11⋊C5
commutator, hypocenterC11C22×C3×C5×C13
FrattiniC1G
Fitting, socleC22×C3×C11×C13C5
LCSG ▷ C11
UCSC1 ◁ C22×C3×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C11⋊C5×C13⋊C9, C13×C22⋊C9×C11⋊C5, C11⋊C5×C22⋊(C13⋊C9), …
maximal normal subgroup ofC22×C11⋊C5×C13⋊C9, C13×C22⋊C9×C11⋊C5, C11⋊C5×C22⋊(C13⋊C9), …
maximal quotient ofC22×C9×C13×C11⋊C5, C2×C3×D3×C13×C11⋊C5, C22×C32×C13×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 91);