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C5×(C157⋊C3)⋊C13 #44499508

order30615
automorphism?
homologyAbelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C157⋊C3)⋊C13
unambiguous semidirect product(C157⋊C3)⋊(C5×C13)
unambiguous semidirect product(C157⋊C13)⋊(C3×C5)
unambiguous semidirect product(C5×C157⋊C3)⋊C13
unambiguous semidirect product(C5×C157⋊C13)⋊C3

Splittings

Fitting, socle, HallC5×C157 ⋊ C3×C13
derived, SylowC157 ⋊ C3×C5×C13
HallC5×C157⋊C13 ⋊ C3
HallC5×C157⋊C3 ⋊ C13
HallC157⋊C13 ⋊ C3×C5
HallC157⋊C3 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC5(C157⋊C3)⋊C13
commutator, cosocle, hypocenterC157C3×C5×C13
FrattiniC1G
Fitting, socleC5×C157C3×C13
LCSG ▷ C157
UCSC1 ◁ C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 785

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30615, 7);