Finite Group Databasebeta

C13×#14558784 #44527591

order31122
automorphism?
homologyAbelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#14558784

Splittings

derived, HallC7×C19 ⋊ C2×C9×C13
HallC13×#11924776 ⋊ C2
HallC13×D7×C19 ⋊ C9
HallC7×C13×C19 ⋊ C2×C9
Hall#11924776 ⋊ C2×C13
HallD7×C19 ⋊ C9×C13
HallC13×C19 ⋊ D7⋊C9
HallC13×D7 ⋊ #4294
HallC7×C13 ⋊ C2×#4294
SylowC19 ⋊ C13×D7⋊C9
HallD7 ⋊ C13×#4294
SylowC7 ⋊ C2×C13×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C13#11716325
commutator, hypocenterC7×C19C2×C9×C13
FrattiniC3C13×#11716325
Fitting, socleC3×C7×C13×C19C2×C3
prime radicalC3×C13×D7×C19C3
cosocleC3×C7×C19C2×C3×C13
LCSG ▷ C7×C19
UCSC1 ◁ C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

1443 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 74);