Finite Group Databasebeta

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C13×C3⋊D399 #44528043

order31122
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C3

Aliases

direct productC13×C3⋊D399
unambiguous semidirect productC3⋊(C13×D399)
unambiguous semidirect productC7⋊(C13×C3⋊D57)
unambiguous semidirect productC19⋊(C13×C3⋊D21)

Splittings

Fitting, socle, HallC32×C7×C13×C19 ⋊ C2
derived, HallC32×C7×C19 ⋊ C2×C13
HallC32×C13×C19 ⋊ D7
HallC7×C13×C19 ⋊ C3⋊D3
HallC32×C7×C13 ⋊ D19
HallC13×C19 ⋊ C3⋊D21
HallC32×C19 ⋊ C13×D7
HallC7×C19 ⋊ C13×C3⋊D3
HallC32×C13 ⋊ D133
HallC7×C13 ⋊ C3⋊D57
HallC32×C7 ⋊ C13×D19
SylowC19 ⋊ C13×C3⋊D21
SylowC32 ⋊ C13×D133
SylowC7 ⋊ C13×C3⋊D57

Subgroups

subgroupG/H
center, hypercenterC13C3⋊D399
commutator, cosocle, hypocenterC32×C7×C19C2×C13
FrattiniC1G
Fitting, socleC32×C7×C13×C19C2
LCSG ▷ C32×C7×C19
UCSC1 ◁ C13

96 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, 526);