Finite Group Databasebeta

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C3×D5×C17×C29 #28414403

order14790
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C17×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C17×C29
unambiguous semidirect productC5⋊(C2×C3×C17×C29)

Splittings

Fitting, socle, HallC3×C5×C17×C29 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C17×C29
HallC5×C17×C29 ⋊ C2×C3
HallC3×C5×C29 ⋊ C2×C17
HallC3×C5×C17 ⋊ C2×C29
HallC5×C29 ⋊ C2×C3×C17
HallC5×C17 ⋊ C2×C3×C29
HallC3×C5 ⋊ C2×C17×C29

Subgroups

subgroupG/H
center, hypercenterC3×C17×C29D5
commutator, cosocle, hypocenterC5C2×C3×C17×C29
FrattiniC1G
Fitting, socleC3×C5×C17×C29C2
LCSG ▷ C5
UCSC1 ◁ C3×C17×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7395

Conjugacy classes & character table

5916 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C17×AGL(1,𝔽5)×C29, C3×C17×#10596816, C3×C29×#66774, …
maximal normal subgroup ofC3×C17×AGL(1,𝔽5)×C29, C3×C17×#10596816, C3×C29×#66774, …
maximal quotient ofC3×C17×Dic5×C29, C2×C3×D5×C17×C29

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14790, 5);