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C5×C13×D41⋊C5 #40998552

order26650
automorphism?
homologyAbelianization (H1) = C2×C52×C13 · Schur multiplier (H2) = C5

Aliases

direct productC5×C13×D41⋊C5
unambiguous semidirect productD41⋊(C52×C13)
unambiguous semidirect product(C41⋊C5)⋊(C2×C5×C13)
unambiguous semidirect product(C5×D41)⋊(C5×C13)
unambiguous semidirect product(C13×D41)⋊C52
unambiguous semidirect product(C5×C13×D41)⋊C5

Splittings

Fitting, socleC5×C13×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C2×C52×C13
HallC5×C13×C41⋊C5 ⋊ C2
HallC13×D41 ⋊ C52
HallC5×C41⋊C5 ⋊ C2×C13
HallC13×C41 ⋊ C2×C52
HallD41 ⋊ C52×C13

Subgroups

subgroupG/H
center, hypercenterC5×C13D41⋊C5
commutator, cosocle, hypocenterC41C2×C52×C13
FrattiniC1G
Fitting, socleC5×C13×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C5×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26650, 14);