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C2×D5×C13×C121 #44538103

order31460
automorphism?
homologyAbelianization (H1) = C22×C13×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C13×C121
unambiguous semidirect productC5⋊(C22×C13×C121)
unambiguous semidirect product(C2×C5)⋊(C2×C13×C121)

Splittings

FittingC2×C5×C13×C121 ⋊ C2
derived, SylowC5 ⋊ C22×C13×C121
HallC5×C13×C121 ⋊ C22
HallC5×C121 ⋊ C22×C13
HallC5×C13 ⋊ C22×C121

Subgroups

subgroupG/H
center, hypercenterC2×C13×C121D5
commutator, hypocenterC5C22×C13×C121
FrattiniC11C2×D5×C11×C13
FittingC2×C5×C13×C121C2
socleC2×C5×C11×C13C2×C11
prime radicalC2×D5×C11×C13C11
cosocleC5×C11C22×C11×C13
LCSG ▷ C5
UCSC1 ◁ C2×C13×C121

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15730

Conjugacy classes & character table

12584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 43);