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(C13⋊C3)⋊(D61⋊C5) #37558225

order23790
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C13⋊C3)⋊(D61⋊C5)
unambiguous semidirect product((C13⋊C3)⋊D61)⋊C5

Splittings

Fitting, socle, derived, HallC13×C61 ⋊ C2×C3×C5
HallC13⋊C3×C61⋊C5 ⋊ C2
HallC13⋊(D61⋊C5) ⋊ C3
Hall(C13⋊C3)⋊D61 ⋊ C5
HallC13×C61⋊C5 ⋊ C2×C3
HallC13⋊C3×C61 ⋊ C2×C5
HallD793 ⋊ C3×C5
HallC61⋊C5 ⋊ D13⋊C3
SylowC61 ⋊ C5×D13⋊C3
HallC13⋊C3 ⋊ D61⋊C5
SylowC13 ⋊ C3×D61⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C61C2×C3×C5
LCSG ▷ C13×C61
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 793

Polycyclic presentation:

2,3,5,13,61|d^a=d^12,e^a=e^60,d^b=d^3,e^c=e^9

Conjugacy classes & character table

82 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 70);