Finite Group Databasebeta

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C11×D805 #31799322

order17710
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D805
unambiguous semidirect productC5⋊(C11×D161)
unambiguous semidirect productC7⋊(C11×D115)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C2
derived, HallC5×C7×C23 ⋊ C2×C11
HallC7×C11×C23 ⋊ D5
HallC5×C11×C23 ⋊ D7
HallC5×C7×C11 ⋊ D23
HallC11×C23 ⋊ D35
HallC7×C23 ⋊ D5×C11
HallC5×C23 ⋊ C11×D7
HallC7×C11 ⋊ D115
HallC5×C11 ⋊ D161
HallC5×C7 ⋊ C11×D23
SylowC23 ⋊ C11×D35
SylowC7 ⋊ C11×D115
SylowC5 ⋊ C11×D161

Subgroups

subgroupG/H
center, hypercenterC11D805
commutator, cosocle, hypocenterC5×C7×C23C2×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C23C2
LCSG ▷ C5×C7×C23
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

4444 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D23×D35, D11×D805, D253⋊D35, …
maximal normal subgroup ofC11×D23×D35, D11×D805, D253⋊D35, …
maximal quotient ofC11×Dic805, C2×C11×D805

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 16);