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C5×C29×D39 #26015191

order11310
isoclinismisoclinic class of D39
automorphism?
homologyAbelianization (H1) = C2×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×D39
unambiguous semidirect productC3⋊(C5×D13×C29)
unambiguous semidirect productC13⋊(C5×D3×C29)

Splittings

Fitting, socle, HallC3×C5×C13×C29 ⋊ C2
derived, HallC3×C13 ⋊ C2×C5×C29
HallC5×C13×C29 ⋊ D3
HallC3×C13×C29 ⋊ C2×C5
HallC3×C5×C29 ⋊ D13
HallC13×C29 ⋊ C5×D3
HallC3×C5×C13 ⋊ C2×C29
HallC3×C29 ⋊ C5×D13
HallC5×C13 ⋊ D3×C29
HallC3×C5 ⋊ D13×C29
SylowC13 ⋊ C5×D3×C29
SylowC3 ⋊ C5×D13×C29

Subgroups

subgroupG/H
center, hypercenterC5×C29D39
commutator, cosocle, hypocenterC3×C13C2×C5×C29
FrattiniC1G
Fitting, socleC3×C5×C13×C29C2
LCSG ▷ C3×C13
UCSC1 ◁ C5×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3045 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D29×D39, C5×D3×D13×C29, C5×D39⋊D29, …
maximal normal subgroup ofC5×D29×D39, C5×D3×D13×C29, C5×D39⋊D29, …
maximal quotient ofC5×C29×Dic39, C2×C5×C29×D39, C5×C29×D117, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11310, 12);