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C3×C13×C61⋊C5 #26045313

order11895
isoclinismisoclinic class of C61⋊C5
automorphism?
homologyAbelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C61⋊C5
unambiguous semidirect product(C3×C61)⋊(C5×C13)
unambiguous semidirect product(C3×C13×C61)⋊C5

Splittings

Fitting, socle, HallC3×C13×C61 ⋊ C5
derived, SylowC61 ⋊ C3×C5×C13
HallC13×C61 ⋊ C3×C5
HallC3×C61 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC3×C13C61⋊C5
commutator, cosocle, hypocenterC61C3×C5×C13
FrattiniC1G
Fitting, socleC3×C13×C61C5
LCSG ▷ C61
UCSC1 ◁ C3×C13

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

663 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×C13×C61⋊C5, C3×C13×D61⋊C5, C3×D13×C61⋊C5, …
maximal normal subgroup ofC2×C3×C13×C61⋊C5, C3×C13×D61⋊C5, C3×D13×C61⋊C5, …
maximal quotient ofC2×C3×C13×C61⋊C5, C9×C13×C61⋊C5, C32×C13×C61⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11895, 2);