Finite Group Databasebeta

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C5×(C19⋊C3)⋊#1181 #45683262

order33060
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C19⋊C3)⋊#1181
unambiguous semidirect product(C19⋊C3)⋊(C5×#1181)
unambiguous semidirect product(C19⋊#1181)⋊(C3×C5)
unambiguous semidirect product(C5×C19⋊#1181)⋊C3

Splittings

Fitting, socle, HallC5×C19×C29 ⋊ C3×C4
derived, HallC19×C29 ⋊ C3×C4×C5
HallC5×C19⋊#1181 ⋊ C3
HallC5×C29×C19⋊C3 ⋊ C4
HallC19⋊#1181 ⋊ C3×C5
HallC29×C19⋊C3 ⋊ C4×C5
HallC5×C19⋊C3 ⋊ #1181
HallC5×C29 ⋊ (C19⋊C3)⋊C4
HallC5×C19 ⋊ C3×#1181
HallC19⋊C3 ⋊ C5×#1181
SylowC29 ⋊ C5×(C19⋊C3)⋊C4
SylowC19 ⋊ C3×C5×#1181

Subgroups

subgroupG/H
center, hypercenterC5(C19⋊C3)⋊#1181
commutator, hypocenterC19×C29C3×C4×C5
FrattiniC1G
Fitting, socleC5×C19×C29C3×C4
prime radicalC5×C19⋊C3×D29C2
cosocleC19×D29C2×C3×C5
LCSG ▷ C19×C29
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2755

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 26);