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C13×D915 #37558178

order23790
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D915
unambiguous semidirect productC3⋊(C13×D305)
unambiguous semidirect productC5⋊(C13×D183)
unambiguous semidirect productC61⋊(C13×D15)

Splittings

Fitting, socle, HallC3×C5×C13×C61 ⋊ C2
derived, HallC3×C5×C61 ⋊ C2×C13
HallC5×C13×C61 ⋊ D3
HallC3×C13×C61 ⋊ D5
HallC13×C61 ⋊ D15
HallC5×C61 ⋊ D3×C13
HallC3×C5×C13 ⋊ D61
HallC3×C61 ⋊ D5×C13
HallC5×C13 ⋊ D183
SylowC61 ⋊ C13×D15
HallC3×C13 ⋊ D305
HallC3×C5 ⋊ C13×D61
SylowC5 ⋊ C13×D183
SylowC3 ⋊ C13×D305

Subgroups

subgroupG/H
center, hypercenterC13D915
commutator, cosocle, hypocenterC3×C5×C61C2×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C61C2
LCSG ▷ C3×C5×C61
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11895

Conjugacy classes & character table

5967 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 23);