Finite Group Databasebeta

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C11×A4×C11⋊C5 #20300029

order7260
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×A4×C11⋊C5
unambiguous semidirect productC22⋊(C3×C11×C11⋊C5)
unambiguous semidirect productC11⋊(C5×C11×A4)
unambiguous semidirect product(C11×A4)⋊(C5×C11)
unambiguous semidirect product(C22×C11⋊C5)⋊(C3×C11)
unambiguous semidirect product(C22×C11×C11⋊C5)⋊C3

Splittings

Fitting, socle, HallC22×C112 ⋊ C3×C5
derivedC22×C11 ⋊ C3×C5×C11
HallC22×C11×C11⋊C5 ⋊ C3
HallC112×A4 ⋊ C5
SylowC112 ⋊ C5×A4
SylowC22 ⋊ C3×C11×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC11A4×C11⋊C5
commutator, hypocenterC22×C11C3×C5×C11
FrattiniC1G
Fitting, socleC22×C112C3×C5
LCSG ▷ C22×C11
UCSC1 ◁ C11

50 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×A4×C11⋊C5, A4×C11⋊C52, C5×C11×A4×C11⋊C5, …
maximal normal subgroup ofC3×C11×A4×C11⋊C5, A4×C11⋊C52, C5×C11×A4×C11⋊C5
maximal quotient ofC11×C22⋊C9×C11⋊C5, C3×C11×A4×C11⋊C5, C11×A4×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 129);