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C2×C5×C13×C13⋊C9 #29503590

order15210
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C13×C13⋊C9
unambiguous semidirect product(C2×C13)⋊(C5×C9×C13)
unambiguous semidirect product(C2×C5×C13)⋊(C9×C13)

Splittings

derivedC13 ⋊ C2×C5×C9×C13
HallC2×C5×C132 ⋊ C9
HallC5×C132 ⋊ C2×C9
HallC2×C132 ⋊ C5×C9
SylowC132 ⋊ C2×C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C13C13⋊C3
commutator, hypocenterC13C2×C5×C9×C13
FrattiniC3C2×C5×C13×C13⋊C3
Fitting, socle, prime radicalC2×C3×C5×C132C3
cosocleC3×C13C2×C3×C5×C13
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1170

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C13×Dic13⋊C9, C5×#20258756, C5×Dic13×C13⋊C9, …
maximal normal subgroup ofC5×C13×Dic13⋊C9, C5×#20258756, C5×Dic13×C13⋊C9, …
maximal quotient ofC4×C5×C13×C13⋊C9, C22×C5×C13×C13⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 53);