Finite Group Databasebeta

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C29×D105 #20259031

order6090
isoclinismisoclinic class of D105
automorphism?
homologyAbelianization (H1) = C2×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D105
unambiguous semidirect productC3⋊(C29×D35)
unambiguous semidirect productC5⋊(C29×D21)
unambiguous semidirect productC7⋊(C29×D15)

Splittings

Fitting, socle, HallC3×C5×C7×C29 ⋊ C2
derived, HallC3×C5×C7 ⋊ C2×C29
HallC5×C7×C29 ⋊ D3
HallC3×C7×C29 ⋊ D5
HallC3×C5×C29 ⋊ D7
HallC7×C29 ⋊ D15
HallC5×C29 ⋊ D21
HallC3×C29 ⋊ D35
HallC5×C7 ⋊ D3×C29
HallC3×C7 ⋊ D5×C29
HallC3×C5 ⋊ D7×C29
SylowC7 ⋊ C29×D15
SylowC5 ⋊ C29×D21
SylowC3 ⋊ C29×D35

Subgroups

subgroupG/H
center, hypercenterC29D105
commutator, hypocenterC3×C5×C7C2×C29
FrattiniC1G
Fitting, socleC3×C5×C7×C29C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1566 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC29×D315, C29×C3⋊(C5⋊AGL(1,𝔽7)), C29×C3⋊D105, …
maximal normal subgroup ofC29×C3⋊(C5⋊AGL(1,𝔽7)), C3×C29×D105, C5×C29×D105
maximal quotient ofC29×D315, C29×C3⋊D105, C3×C29×D105, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6090, 17);