Finite Group Databasebeta

← Prev (#45683258) Next (#45683260) →

C29×(C19⋊C3)⋊Dic5 #45683259

order33060
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×(C19⋊C3)⋊Dic5
unambiguous semidirect product(C19⋊C3)⋊(Dic5×C29)
unambiguous semidirect productDic95⋊(C3×C29)
unambiguous semidirect product(C29×Dic95)⋊C3

Splittings

derived, HallC5×C19 ⋊ C3×C4×C29
HallC29×Dic95 ⋊ C3
HallC5×C29×C19⋊C3 ⋊ C4
HallC5×C19×C29 ⋊ C3×C4
HallC29×C19⋊C3 ⋊ Dic5
HallC19×C29 ⋊ C3×Dic5
HallDic95 ⋊ C3×C29
HallC5×C19⋊C3 ⋊ C4×C29
HallC5×C29 ⋊ (C19⋊C3)⋊C4
HallC19⋊C3 ⋊ Dic5×C29
SylowC19 ⋊ C3×Dic5×C29
SylowC5 ⋊ C29×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C29C5⋊(D19⋊C3)
commutator, hypocenterC5×C19C3×C4×C29
FrattiniC2C29×C5⋊(D19⋊C3)
Fitting, socleC2×C5×C19×C29C2×C3
prime radicalC2×C5×C29×C19⋊C3C2
cosocleC2×C5×C19C2×C3×C29
LCSG ▷ C5×C19
UCSC1 ◁ C2×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11020

Conjugacy classes & character table

1566 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 23);