Finite Group Databasebeta

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C3×C17×D145 #28414404

order14790
isoclinismisoclinic class of D145
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×D145
unambiguous semidirect productC5⋊(C3×C17×D29)
unambiguous semidirect productC29⋊(C3×D5×C17)

Splittings

Fitting, socle, HallC3×C5×C17×C29 ⋊ C2
derived, HallC5×C29 ⋊ C2×C3×C17
HallC5×C17×C29 ⋊ C2×C3
HallC3×C17×C29 ⋊ D5
HallC17×C29 ⋊ C3×D5
HallC3×C5×C29 ⋊ C2×C17
HallC3×C5×C17 ⋊ D29
HallC3×C29 ⋊ D5×C17
HallC5×C17 ⋊ C3×D29
SylowC29 ⋊ C3×D5×C17
HallC3×C5 ⋊ C17×D29
SylowC5 ⋊ C3×C17×D29

Subgroups

subgroupG/H
center, hypercenterC3×C17D145
commutator, cosocle, hypocenterC5×C29C2×C3×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C29C2
LCSG ▷ C5×C29
UCSC1 ◁ C3×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7395

Conjugacy classes & character table

3774 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C17×#10596814, C3×C17×#10596815, C3×#23754497, …
maximal normal subgroup ofC3×C17×#10596814, C3×C17×#10596815, C3×#23754497, …
maximal quotient ofC3×C17×Dic145, C2×C3×C17×D145

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14790, 6);