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C19×D935 #48001051

order35530
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×D935
unambiguous semidirect productC5⋊(C19×D187)
unambiguous semidirect productC11⋊(C19×D85)
unambiguous semidirect productC17⋊(C19×D55)

Splittings

Fitting, socle, HallC5×C11×C17×C19 ⋊ C2
derived, HallC5×C11×C17 ⋊ C2×C19
HallC11×C17×C19 ⋊ D5
HallC5×C17×C19 ⋊ D11
HallC5×C11×C19 ⋊ D17
HallC17×C19 ⋊ D55
HallC11×C19 ⋊ D85
HallC11×C17 ⋊ D5×C19
HallC5×C19 ⋊ D187
HallC5×C17 ⋊ C19×D11
HallC5×C11 ⋊ C19×D17
SylowC17 ⋊ C19×D55
SylowC11 ⋊ C19×D85
SylowC5 ⋊ C19×D187

Subgroups

subgroupG/H
center, hypercenterC19D935
commutator, cosocle, hypocenterC5×C11×C17C2×C19
FrattiniC1G
Fitting, socleC5×C11×C17×C19C2
LCSG ▷ C5×C11×C17
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17765

Conjugacy classes & character table

8911 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 16);