Finite Group Databasebeta

← Prev (#27130959) Next (#27130961) →

C22×C5×C11×C11⋊C5 #27130960

order12100
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C52×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C5×C11×C11⋊C5
unambiguous semidirect product(C22×C11)⋊(C52×C11)
unambiguous semidirect product(C22×C5×C11)⋊(C5×C11)

Splittings

Fitting, socleC22×C5×C112 ⋊ C5
derivedC11 ⋊ C22×C52×C11
HallC22×C112 ⋊ C52
SylowC112 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC22×C5×C11C11⋊C5
commutator, cosocle, hypocenterC11C22×C52×C11
FrattiniC1G
Fitting, socleC22×C5×C112C5
LCSG ▷ C11
UCSC1 ◁ C22×C5×C11

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×A4×C11⋊C5, C2×C5×D3×C11×C11⋊C5, C22×C3×C5×C11×C11⋊C5
maximal normal subgroup ofC5×C11×A4×C11⋊C5, C22×C3×C5×C11×C11⋊C5
maximal quotient ofC2×C5×D3×C11×C11⋊C5, C22×C3×C5×C11×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 239);