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C7×D11×C13⋊C3 #20238797

order6006
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D11×C13⋊C3
unambiguous semidirect productC11⋊(C2×C7×C13⋊C3)
unambiguous semidirect product(C13×D11)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C2×C3
derived, HallC11×C13 ⋊ C2×C3×C7
HallC7×C11×C13⋊C3 ⋊ C2
HallC7×C13×D11 ⋊ C3
HallC11×C13⋊C3 ⋊ C2×C7
HallC13×D11 ⋊ C3×C7
HallC7×C13 ⋊ C3×D11
HallC7×C11 ⋊ C2×C13⋊C3
SylowC13 ⋊ C3×C7×D11
SylowC11 ⋊ C2×C7×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D11×C13⋊C3
commutator, hypocenterC11×C13C2×C3×C7
FrattiniC1G
Fitting, socleC7×C11×C13C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

343 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D11×D13⋊C3, D11×(C13⋊C3)⋊D7, D7×D11×C13⋊C3, …
maximal normal subgroup ofC7×D11×D13⋊C3, D11×(C13⋊C3)⋊D7, D7×D11×C13⋊C3, …
maximal quotient ofC7×C13⋊C3×Dic11, C2×C7×D11×C13⋊C3, C7×D11×C13⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6006, 25);