Finite Group Databasebeta

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C13×Dic121⋊C5 #44538063

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

Aliases

direct productC13×Dic121⋊C5
unambiguous semidirect productDic121⋊(C5×C13)
unambiguous semidirect product(C121⋊C5)⋊(C4×C13)
unambiguous semidirect product(C13×Dic121)⋊C5

Splittings

derived, SylowC121 ⋊ C4×C5×C13
HallC13×C121⋊C5 ⋊ C4
HallC13×Dic121 ⋊ C5
HallC13×C121 ⋊ C4×C5
HallC121⋊C5 ⋊ C4×C13
HallDic121 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D121⋊C5
commutator, hypocenterC121C4×C5×C13
FrattiniC2×C11C13×AGL(1,𝔽11)
FittingC2×C13×C121C2×C5
socleC2×C11×C13AGL(1,𝔽11)
prime radicalC2×C13×C121⋊C5C2
cosocleC2×C121C2×C5×C13
LCSG ▷ C121
UCSC1 ◁ C2×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6292

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 3);