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C29×D255 #28414413

order14790
isoclinismisoclinic class of D255
automorphism?
homologyAbelianization (H1) = C2×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D255
unambiguous semidirect productC3⋊(C29×D85)
unambiguous semidirect productC5⋊(C29×D51)
unambiguous semidirect productC17⋊(C29×D15)

Splittings

Fitting, socle, HallC3×C5×C17×C29 ⋊ C2
derived, HallC3×C5×C17 ⋊ C2×C29
HallC5×C17×C29 ⋊ D3
HallC3×C17×C29 ⋊ D5
HallC17×C29 ⋊ D15
HallC3×C5×C29 ⋊ D17
HallC5×C29 ⋊ D51
HallC3×C29 ⋊ D85
HallC5×C17 ⋊ D3×C29
HallC3×C17 ⋊ D5×C29
SylowC17 ⋊ C29×D15
HallC3×C5 ⋊ C29×D17
SylowC5 ⋊ C29×D51
SylowC3 ⋊ C29×D85

Subgroups

subgroupG/H
center, hypercenterC29D255
commutator, cosocle, hypocenterC3×C5×C17C2×C29
FrattiniC1G
Fitting, socleC3×C5×C17×C29C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7395

Conjugacy classes & character table

3741 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD29×D255, C29×D15×D17, D493⋊D15, …
maximal normal subgroup ofD29×D255, C29×D15×D17, D493⋊D15, …
maximal quotient ofC29×Dic255, C2×C29×D255

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14790, 15);