Finite Group Databasebeta

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C5×Dic59⋊C29 #46803755

order34220
automorphism?
homologyAbelianization (H1) = C4×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic59⋊C29
unambiguous semidirect productDic59⋊(C5×C29)
unambiguous semidirect product(C5×Dic59)⋊C29
unambiguous semidirect product(C59⋊C29)⋊(C4×C5)

Splittings

derived, SylowC59 ⋊ C4×C5×C29
HallC5×C59⋊C29 ⋊ C4
HallC59⋊C29 ⋊ C4×C5
HallC5×Dic59 ⋊ C29
HallC5×C59 ⋊ C4×C29
HallDic59 ⋊ C5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5AGL(1,𝔽59)
commutator, hypocenterC59C4×C5×C29
FrattiniC2C5×AGL(1,𝔽59)
Fitting, socleC2×C5×C59C2×C29
prime radicalC2×C5×C59⋊C29C2
cosocleC2×C59C2×C5×C29
LCSG ▷ C59
UCSC1 ◁ C2×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1180

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34220, 10);