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C3×D1001 #20238784

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

Aliases

direct productC3×D1001
unambiguous semidirect productC11⋊(C3×D91)

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C2
derived, HallC7×C11×C13 ⋊ C2×C3
HallC3×C11×C13 ⋊ D7
HallC3×C7×C13 ⋊ D11
HallC3×C7×C11 ⋊ D13
HallC11×C13 ⋊ C3×D7
HallC7×C13 ⋊ C3×D11
HallC7×C11 ⋊ C3×D13
HallC3×C13 ⋊ D77
HallC3×C11 ⋊ D91
HallC3×C7 ⋊ D143
SylowC13 ⋊ C3×D77
SylowC11 ⋊ C3×D91
SylowC7 ⋊ C3×D143

Subgroups

subgroupG/H
center, hypercenterC3D1001
commutator, hypocenterC7×C11×C13C2×C3
FrattiniC1G
Fitting, socleC3×C7×C11×C13C2
LCSG ▷ C7×C11×C13
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1506 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D13×D77, C3×D11×D91, C3×D7×D143, …
maximal normal subgroup ofC3×D13×D77, C3×D11×D91, C3×D7×D143, …
maximal quotient ofC3×Dic1001, C2×C3×D1001, C9×D1001, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6006, 12);