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C13×(D61⋊C3)⋊C5 #37558216

order23790
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×(D61⋊C3)⋊C5
unambiguous semidirect product(D61⋊C3)⋊(C5×C13)
unambiguous semidirect product(D61⋊C5)⋊(C3×C13)
unambiguous semidirect product((C61⋊C3)⋊C5)⋊(C2×C13)
unambiguous semidirect product(C13×D61⋊C3)⋊C5

Splittings

Fitting, socle, HallC13×C61 ⋊ C2×C3×C5
derived, SylowC61 ⋊ C2×C3×C5×C13
HallC13×(C61⋊C3)⋊C5 ⋊ C2
HallC13×D61⋊C5 ⋊ C3
HallC13×D61⋊C3 ⋊ C5
HallC13×C61⋊C5 ⋊ C2×C3
HallC13×C61⋊C3 ⋊ C2×C5
HallC13×D61 ⋊ C3×C5
Hall(C61⋊C3)⋊C5 ⋊ C2×C13
HallD61⋊C5 ⋊ C3×C13
HallD61⋊C3 ⋊ C5×C13
HallC61⋊C5 ⋊ C2×C3×C13
HallC61⋊C3 ⋊ C2×C5×C13
HallD61 ⋊ C3×C5×C13

Subgroups

subgroupG/H
center, hypercenterC13(D61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C2×C3×C5×C13
FrattiniC1G
Fitting, socleC13×C61C2×C3×C5
LCSG ▷ C61
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 793

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 61);