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C19×D595 #36383045

order22610
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×D595
unambiguous semidirect productC5⋊(C19×D119)
unambiguous semidirect productC7⋊(C19×D85)
unambiguous semidirect productC17⋊(C19×D35)

Splittings

Fitting, socle, HallC5×C7×C17×C19 ⋊ C2
derived, HallC5×C7×C17 ⋊ C2×C19
HallC7×C17×C19 ⋊ D5
HallC5×C17×C19 ⋊ D7
HallC5×C7×C19 ⋊ D17
HallC17×C19 ⋊ D35
HallC7×C19 ⋊ D85
HallC7×C17 ⋊ D5×C19
HallC5×C19 ⋊ D119
HallC5×C17 ⋊ D7×C19
HallC5×C7 ⋊ C19×D17
SylowC17 ⋊ C19×D35
SylowC7 ⋊ C19×D85
SylowC5 ⋊ C19×D119

Subgroups

subgroupG/H
center, hypercenterC19D595
commutator, cosocle, hypocenterC5×C7×C17C2×C19
FrattiniC1G
Fitting, socleC5×C7×C17×C19C2
LCSG ▷ C5×C7×C17
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11305

Conjugacy classes & character table

5681 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22610, 15);