Finite Group Databasebeta

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C4×C13×C121⋊C5 #44538065

order31460
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×C121⋊C5
unambiguous semidirect product(C4×C121)⋊(C5×C13)
unambiguous semidirect product(C4×C13×C121)⋊C5

Splittings

Fitting, HallC4×C13×C121 ⋊ C5
derived, SylowC121 ⋊ C4×C5×C13
HallC13×C121 ⋊ C4×C5
HallC4×C121 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC4×C13C121⋊C5
commutator, hypocenterC121C4×C5×C13
FrattiniC2×C11C2×C13×C11⋊C5
FittingC4×C13×C121C5
socleC2×C11×C13C2×C11⋊C5
prime radicalC2×C13×C121⋊C5C2
cosocleC2×C121C2×C5×C13
LCSG ▷ C121
UCSC1 ◁ C4×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6292

Conjugacy classes & character table

1508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 5);