Finite Group Databasebeta

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C13×Dic735 #50303333

order38220
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic735
unambiguous semidirect productC3⋊(C13×Dic245)
unambiguous semidirect productC49⋊(C13×Dic15)

Splittings

derived, HallC3×C5×C49 ⋊ C4×C13
HallC3×C5×C13×C49 ⋊ C4
HallC5×C13×C49 ⋊ Dic3
HallC3×C13×C49 ⋊ Dic5
HallC13×C49 ⋊ Dic15
HallC5×C49 ⋊ Dic3×C13
HallC3×C5×C13 ⋊ Dic49
HallC3×C49 ⋊ C13×Dic5
HallC5×C13 ⋊ Dic147
SylowC49 ⋊ C13×Dic15
HallC3×C13 ⋊ Dic245
HallC3×C5 ⋊ C13×Dic49
SylowC5 ⋊ C13×Dic147
SylowC3 ⋊ C13×Dic245

Subgroups

subgroupG/H
center, hypercenterC2×C13D735
commutator, hypocenterC3×C5×C49C4×C13
FrattiniC2×C7C13×D105
FittingC2×C3×C5×C13×C49C2
socle, prime radicalC2×C3×C5×C7×C13D7
cosocleC2×C3×C5×C49C2×C13
LCSG ▷ C3×C5×C49
UCSC1 ◁ C2×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38220

Conjugacy classes & character table

9594 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 19);