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C11×D819 #31824973

order18018
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D819
unambiguous semidirect productC7⋊(C11×D117)
unambiguous semidirect productC9⋊(C11×D91)
unambiguous semidirect productC13⋊(C11×D63)

Splittings

Fitting, HallC7×C9×C11×C13 ⋊ C2
derived, HallC7×C9×C13 ⋊ C2×C11
HallC9×C11×C13 ⋊ D7
HallC7×C11×C13 ⋊ D9
HallC7×C9×C11 ⋊ D13
HallC11×C13 ⋊ D63
HallC9×C13 ⋊ C11×D7
HallC9×C11 ⋊ D91
HallC7×C13 ⋊ C11×D9
HallC7×C11 ⋊ D117
HallC7×C9 ⋊ C11×D13
SylowC13 ⋊ C11×D63
SylowC9 ⋊ C11×D91
SylowC7 ⋊ C11×D117

Subgroups

subgroupG/H
center, hypercenterC11D819
commutator, cosocle, hypocenterC7×C9×C13C2×C11
FrattiniC3C11×D273
FittingC7×C9×C11×C13C2
socleC3×C7×C11×C13D3
LCSG ▷ C7×C9×C13
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

4521 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D13×D63, D11×D819, D143⋊D63, …
maximal normal subgroup ofC11×D13×D63, D11×D819, D143⋊D63, …
maximal quotient ofC11×Dic819, C2×C11×D819

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 18);