Finite Group Databasebeta

C7×#17984623 #44527575

order31122
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×#17984623

Splittings

derived, HallC13×C19 ⋊ C2×C7×C9
HallC7×#14555735 ⋊ C2
HallC7×D247 ⋊ C9
Hall#14555735 ⋊ C2×C7
HallC7×C13×C19 ⋊ C2×C9
HallD247 ⋊ C7×C9
HallC7×C19 ⋊ D13⋊C9
HallC7×C13 ⋊ #4294⋊C2
SylowC19 ⋊ C7×D13⋊C9
SylowC13 ⋊ C7×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C7#13093366
commutator, hypocenterC13×C19C2×C7×C9
FrattiniC3C7×#13093366
Fitting, socleC3×C7×C13×C19C2×C3
prime radicalC3×C7×D247C3
cosocleC3×C13×C19C2×C3×C7
LCSG ▷ C13×C19
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 58);