Finite Group Databasebeta

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C11×C17×D95 #48001046

order35530
automorphism?
homologyAbelianization (H1) = C2×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×D95
unambiguous semidirect productC5⋊(C11×C17×D19)
unambiguous semidirect productC19⋊(D5×C11×C17)

Splittings

Fitting, socle, HallC5×C11×C17×C19 ⋊ C2
derived, HallC5×C19 ⋊ C2×C11×C17
HallC11×C17×C19 ⋊ D5
HallC5×C17×C19 ⋊ C2×C11
HallC5×C11×C19 ⋊ C2×C17
HallC5×C11×C17 ⋊ D19
HallC17×C19 ⋊ D5×C11
HallC11×C19 ⋊ D5×C17
HallC5×C17 ⋊ C11×D19
HallC5×C11 ⋊ C17×D19
SylowC19 ⋊ D5×C11×C17
SylowC5 ⋊ C11×C17×D19

Subgroups

subgroupG/H
center, hypercenterC11×C17D95
commutator, cosocle, hypocenterC5×C19C2×C11×C17
FrattiniC1G
Fitting, socleC5×C11×C17×C19C2
LCSG ▷ C5×C19
UCSC1 ◁ C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17765

Conjugacy classes & character table

9163 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 11);