Finite Group Databasebeta

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C3×C29×D31⋊C5 #41004201

order26970
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C29×D31⋊C5
unambiguous semidirect product(C3×D31)⋊(C5×C29)
unambiguous semidirect product(C3×C29×D31)⋊C5

Splittings

Fitting, socle, HallC3×C29×C31 ⋊ C2×C5
derived, SylowC31 ⋊ C2×C3×C5×C29
HallC3×C29×ΓL(1,𝔽32) ⋊ C2
HallC3×C29×D31 ⋊ C5
HallC29×ΓL(1,𝔽32) ⋊ C2×C3
HallC29×D31 ⋊ C3×C5
HallC29×C31 ⋊ C2×C3×C5
HallC3×ΓL(1,𝔽32) ⋊ C2×C29
HallC3×D31 ⋊ C5×C29
HallΓL(1,𝔽32) ⋊ C2×C3×C29
HallC3×C31 ⋊ C2×C5×C29
HallD31 ⋊ C3×C5×C29

Subgroups

subgroupG/H
center, hypercenterC3×C29D31⋊C5
commutator, cosocle, hypocenterC31C2×C3×C5×C29
FrattiniC1G
Fitting, socleC3×C29×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C3×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2697

Conjugacy classes & character table

1131 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 20);