Finite Group Databasebeta

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C31×D435 #41004199

order26970
automorphism?
homologyAbelianization (H1) = C2×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×D435
unambiguous semidirect productC3⋊(C31×D145)
unambiguous semidirect productC5⋊(C31×D87)
unambiguous semidirect productC29⋊(D15×C31)

Splittings

Fitting, socle, HallC3×C5×C29×C31 ⋊ C2
derived, HallC3×C5×C29 ⋊ C2×C31
HallC5×C29×C31 ⋊ D3
HallC3×C29×C31 ⋊ D5
HallC29×C31 ⋊ D15
HallC3×C5×C31 ⋊ D29
HallC5×C31 ⋊ D87
HallC5×C29 ⋊ D3×C31
HallC3×C31 ⋊ D145
HallC3×C29 ⋊ D5×C31
SylowC29 ⋊ D15×C31
HallC3×C5 ⋊ C31×D29
SylowC5 ⋊ C31×D87
SylowC3 ⋊ C31×D145

Subgroups

subgroupG/H
center, hypercenterC31D435
commutator, cosocle, hypocenterC3×C5×C29C2×C31
FrattiniC1G
Fitting, socleC3×C5×C29×C31C2
LCSG ▷ C3×C5×C29
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13485

Conjugacy classes & character table

6789 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 18);