Finite Group Databasebeta

C7×C13×#4294⋊C2 #44527547

order31122
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×#4294⋊C2
unambiguous semidirect product#4294⋊(C2×C7×C13)

Splittings

derived, SylowC19 ⋊ C2×C7×C9×C13
HallC7×C13×#4294 ⋊ C2
HallC7×C13×D19 ⋊ C9
HallC13×#4294 ⋊ C2×C7
HallC7×C13×C19 ⋊ C2×C9
HallC7×#4294 ⋊ C2×C13
HallC13×D19 ⋊ C7×C9
HallC7×D19 ⋊ C9×C13
HallC13×C19 ⋊ C2×C7×C9
Hall#4294 ⋊ C2×C7×C13
HallC7×C19 ⋊ C2×C9×C13
HallD19 ⋊ C7×C9×C13

Subgroups

subgroupG/H
center, hypercenterC3×C7×C13D19⋊C3
commutator, hypocenterC19C2×C7×C9×C13
FrattiniC3C7×C13×D19⋊C3
Fitting, socleC3×C7×C13×C19C2×C3
prime radicalC3×C7×C13×D19C3
cosocleC3×C19C2×C3×C7×C13
LCSG ▷ C19
UCSC1 ◁ C3×C7×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

2457 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 30);