Finite Group Databasebeta

C19×#13109902 #44527619

order31122
automorphism?
homologyAbelianization (H1) = C2×C9×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×#13109902

Splittings

derived, HallC7×C13 ⋊ C2×C9×C19
HallC19×#11717941 ⋊ C2
HallC19×D91 ⋊ C9
HallC7×C13×C19 ⋊ C2×C9
Hall#11717941 ⋊ C2×C19
HallC13×C19 ⋊ D7⋊C9
HallD91 ⋊ C9×C19
HallC7×C19 ⋊ D13⋊C9
SylowC13 ⋊ C19×D7⋊C9
SylowC7 ⋊ C19×D13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C19#10587722
commutator, hypocenterC7×C13C2×C9×C19
FrattiniC3C19×#10587722
Fitting, socleC3×C7×C13×C19C2×C3
prime radicalC3×C19×D91C3
cosocleC3×C7×C13C2×C3×C19
LCSG ▷ C7×C13
UCSC1 ◁ C3×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

1197 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 102);