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C3×D1309 #21463271

order7854
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D1309
unambiguous semidirect productC11⋊(C3×D119)
unambiguous semidirect productC17⋊(C3×D77)

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C2
derived, HallC7×C11×C17 ⋊ C2×C3
HallC3×C11×C17 ⋊ D7
HallC3×C7×C17 ⋊ D11
HallC3×C7×C11 ⋊ D17
HallC11×C17 ⋊ C3×D7
HallC7×C17 ⋊ C3×D11
HallC7×C11 ⋊ C3×D17
HallC3×C17 ⋊ D77
HallC3×C11 ⋊ D119
HallC3×C7 ⋊ D187
SylowC17 ⋊ C3×D77
SylowC11 ⋊ C3×D119
SylowC7 ⋊ C3×D187

Subgroups

subgroupG/H
center, hypercenterC3D1309
commutator, hypocenterC7×C11×C17C2×C3
FrattiniC1G
Fitting, socleC3×C7×C11×C17C2
LCSG ▷ C7×C11×C17
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1968 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D17×D77, C3×D11×D119, C3×D7×D187, …
maximal normal subgroup ofC3×D17×D77, C3×D11×D119, C3×D7×D187, …
maximal quotient ofC3×Dic1309, C2×C3×D1309, C9×D1309, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7854, 9);