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C13×D1197 #44527544

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

Aliases

direct productC13×D1197
unambiguous semidirect productC7⋊(C13×D171)
unambiguous semidirect productC9⋊(C13×D133)
unambiguous semidirect productC19⋊(C13×D63)

Splittings

Fitting, HallC7×C9×C13×C19 ⋊ C2
derived, HallC7×C9×C19 ⋊ C2×C13
HallC9×C13×C19 ⋊ D7
HallC7×C13×C19 ⋊ D9
HallC7×C9×C13 ⋊ D19
HallC13×C19 ⋊ D63
HallC9×C19 ⋊ C13×D7
HallC7×C19 ⋊ C13×D9
HallC9×C13 ⋊ D133
HallC7×C13 ⋊ D171
HallC7×C9 ⋊ C13×D19
SylowC19 ⋊ C13×D63
SylowC9 ⋊ C13×D133
SylowC7 ⋊ C13×D171

Subgroups

subgroupG/H
center, hypercenterC13D1197
commutator, cosocle, hypocenterC7×C9×C19C2×C13
FrattiniC3C13×D399
FittingC7×C9×C13×C19C2
socleC3×C7×C13×C19D3
LCSG ▷ C7×C9×C19
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

7800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 27);