Finite Group Databasebeta

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C5×D2697 #41004196

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

Aliases

direct productC5×D2697
unambiguous semidirect productC3⋊(C5×D899)
unambiguous semidirect productC29⋊(C5×D93)

Splittings

Fitting, socle, HallC3×C5×C29×C31 ⋊ C2
derived, HallC3×C29×C31 ⋊ C2×C5
HallC5×C29×C31 ⋊ D3
HallC29×C31 ⋊ C5×D3
HallC3×C5×C31 ⋊ D29
HallC3×C5×C29 ⋊ D31
HallC5×C31 ⋊ D87
HallC5×C29 ⋊ D93
HallC3×C31 ⋊ C5×D29
HallC3×C29 ⋊ C5×D31
SylowC31 ⋊ C5×D87
SylowC29 ⋊ C5×D93
HallC3×C5 ⋊ D899
SylowC3 ⋊ C5×D899

Subgroups

subgroupG/H
center, hypercenterC5D2697
commutator, cosocle, hypocenterC3×C29×C31C2×C5
FrattiniC1G
Fitting, socleC3×C5×C29×C31C2
LCSG ▷ C3×C29×C31
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13485

Conjugacy classes & character table

6750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 15);