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C11×C11⋊(D13⋊C3) #22628071

order9438
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C11⋊(D13⋊C3)
unambiguous semidirect productC11⋊(C11×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C11×D11)
unambiguous semidirect productD143⋊(C3×C11)
unambiguous semidirect product(C11×D143)⋊C3

Splittings

Fitting, socle, HallC112×C13 ⋊ C2×C3
derivedC11×C13 ⋊ C2×C3×C11
HallC112×C13⋊C3 ⋊ C2
HallC11×D143 ⋊ C3
SylowC112 ⋊ D13⋊C3
HallC13⋊C3 ⋊ C11×D11
SylowC13 ⋊ C3×C11×D11

Subgroups

subgroupG/H
center, hypercenterC11C11⋊(D13⋊C3)
commutator, hypocenterC11×C13C2×C3×C11
FrattiniC1G
Fitting, socleC112×C13C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C11

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

473 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×D11×D13⋊C3, D11×C11⋊(D13⋊C3), (C11⋊(D13⋊C3))⋊D11, …
maximal normal subgroup ofC11×D11×D13⋊C3, D11×C11⋊(D13⋊C3), (C11⋊(D13⋊C3))⋊D11, …
maximal quotient ofC11×C11⋊(Dic13⋊C3), C2×C11×C11⋊(D13⋊C3), C11×C11⋊(D13⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9438, 15);