Finite Group Databasebeta

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C5×C19×C3⋊#1181 #45683307

order33060
automorphism?
homologyAbelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC5×C19×C3⋊#1181
unambiguous semidirect productC3⋊(C5×C19×#1181)

Splittings

Fitting, socle, HallC3×C5×C19×C29 ⋊ C4
derived, HallC3×C29 ⋊ C4×C5×C19
HallC5×C19×C29 ⋊ Dic3
HallC3×C19×C29 ⋊ C4×C5
HallC19×C29 ⋊ C5×Dic3
HallC3×C5×C29 ⋊ C4×C19
HallC3×C5×C19 ⋊ #1181
HallC5×C29 ⋊ Dic3×C19
HallC3×C19 ⋊ C5×#1181
SylowC29 ⋊ C5×Dic3×C19
HallC3×C5 ⋊ C19×#1181
SylowC3 ⋊ C5×C19×#1181

Subgroups

subgroupG/H
center, hypercenterC5×C19C3⋊#1181
commutator, hypocenterC3×C29C4×C5×C19
FrattiniC1G
Fitting, socleC3×C5×C19×C29C4
prime radicalC3×C5×C19×D29C2
cosocleC3×D29C2×C5×C19
LCSG ▷ C3×C29
UCSC1 ◁ C5×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8265

Conjugacy classes & character table

2565 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 71);