Finite Group Databasebeta

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C5×C11×C17×D19 #48001038

order35530
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C17×D19
unambiguous semidirect productC19⋊(C2×C5×C11×C17)

Splittings

Fitting, socle, HallC5×C11×C17×C19 ⋊ C2
derived, SylowC19 ⋊ C2×C5×C11×C17
HallC11×C17×C19 ⋊ C2×C5
HallC5×C17×C19 ⋊ C2×C11
HallC5×C11×C19 ⋊ C2×C17
HallC17×C19 ⋊ C2×C5×C11
HallC11×C19 ⋊ C2×C5×C17
HallC5×C19 ⋊ C2×C11×C17

Subgroups

subgroupG/H
center, hypercenterC5×C11×C17D19
commutator, cosocle, hypocenterC19C2×C5×C11×C17
FrattiniC1G
Fitting, socleC5×C11×C17×C19C2
LCSG ▷ C19
UCSC1 ◁ C5×C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17765

Conjugacy classes & character table

10285 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 3);