Finite Group Databasebeta

← Prev (#30685301) Next (#30685303) →

C3×C11×D259 #30685302

order17094
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D259

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C2
derived, HallC7×C37 ⋊ C2×C3×C11
HallC7×C11×C37 ⋊ C2×C3
HallC3×C11×C37 ⋊ D7
HallC3×C7×C37 ⋊ C2×C11
HallC11×C37 ⋊ C3×D7
HallC3×C7×C11 ⋊ D37
HallC3×C37 ⋊ C11×D7
HallC7×C11 ⋊ C3×D37
SylowC37 ⋊ C3×C11×D7
HallC3×C7 ⋊ C11×D37
SylowC7 ⋊ C3×C11×D37

Subgroups

subgroupG/H
center, hypercenterC3×C11D259
commutator, cosocle, hypocenterC7×C37C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C37C2
LCSG ▷ C7×C37
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

4323 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×D7×D37, C3×D11×D259, C3×D77⋊D37, …
maximal normal subgroup ofC3×C11×D7×D37, C3×D11×D259, C3×D77⋊D37, …
maximal quotient ofC3×C11×Dic259, C2×C3×C11×D259

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17094, 10);