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C3×C5×C19×D29 #30658342

order16530
isoclinismisoclinic class of D29
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C19×D29
unambiguous semidirect productC29⋊(C2×C3×C5×C19)

Splittings

Fitting, socle, HallC3×C5×C19×C29 ⋊ C2
derived, SylowC29 ⋊ C2×C3×C5×C19
HallC5×C19×C29 ⋊ C2×C3
HallC3×C19×C29 ⋊ C2×C5
HallC19×C29 ⋊ C2×C3×C5
HallC3×C5×C29 ⋊ C2×C19
HallC5×C29 ⋊ C2×C3×C19
HallC3×C29 ⋊ C2×C5×C19

Subgroups

subgroupG/H
center, hypercenterC3×C5×C19D29
commutator, cosocle, hypocenterC29C2×C3×C5×C19
FrattiniC1G
Fitting, socleC3×C5×C19×C29C2
LCSG ▷ C29
UCSC1 ◁ C3×C5×C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8265

Conjugacy classes & character table

4560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C19×#1181, C3×C5×C19⋊#1181, C3×C5×D19×D29, …
maximal normal subgroup ofC3×C5×C19×#1181, C3×C5×C19⋊#1181, C3×C5×D19×D29, …
maximal quotient ofC3×C5×C19×Dic29, C2×C3×C5×C19×D29

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16530, 3);