Finite Group Databasebeta

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C13×C3⋊#10596817 #36383201

order22620
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊#10596817
unambiguous semidirect productC3⋊(C13×#10596817)

Splittings

Fitting, socle, HallC3×C5×C13×C29 ⋊ C4
derived, HallC3×C5×C29 ⋊ C4×C13
HallC5×C13×C29 ⋊ Dic3
HallC3×C13×C29 ⋊ Dic5
HallC13×C29 ⋊ Dic15
HallC3×C5×C13 ⋊ #1181
HallC5×C29 ⋊ Dic3×C13
HallC3×C29 ⋊ C13×Dic5
HallC5×C13 ⋊ C3⋊#1181
HallC3×C13 ⋊ #10596817
SylowC29 ⋊ C13×Dic15
HallC3×C5 ⋊ C13×#1181
SylowC5 ⋊ C13×C3⋊#1181
SylowC3 ⋊ C13×#10596817

Subgroups

subgroupG/H
center, hypercenterC13C3⋊#10596817
commutator, hypocenterC3×C5×C29C4×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C29C4
prime radicalC3×C5×C13×D29C2
cosocleC3×C5×D29C2×C13
LCSG ▷ C3×C5×C29
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5655

Conjugacy classes & character table

1599 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22620, 131);