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C11×(C13⋊C3)⋊D7 #20238809

order6006
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×(C13⋊C3)⋊D7
unambiguous semidirect product(C13⋊C3)⋊(C11×D7)

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C11
HallC7×C11×C13⋊C3 ⋊ C2
HallC11×D91 ⋊ C3
HallC11×C13⋊C3 ⋊ D7
HallC7×C13⋊C3 ⋊ C2×C11
HallD91 ⋊ C3×C11
HallC11×C13 ⋊ C3×D7
HallC7×C11 ⋊ D13⋊C3
HallC13⋊C3 ⋊ C11×D7
SylowC13 ⋊ C3×C11×D7
SylowC7 ⋊ C11×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC11(C13⋊C3)⋊D7
commutator, hypocenterC7×C13C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

319 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×D7×D13⋊C3, D11×(C13⋊C3)⋊D7, ((C13⋊C3)⋊D7)⋊D11, …
maximal normal subgroup ofC11×D7×D13⋊C3, D11×(C13⋊C3)⋊D7, ((C13⋊C3)⋊D7)⋊D11, …
maximal quotient ofC11×#11763955, C2×C11×(C13⋊C3)⋊D7, C11×(C13⋊C9)⋊D7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6006, 37);