Finite Group Databasebeta

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C5×D2679 #40999541

order26790
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2679
unambiguous semidirect productC3⋊(C5×D893)
unambiguous semidirect productC19⋊(C5×D141)
unambiguous semidirect productC47⋊(C5×D57)

Splittings

Fitting, socle, HallC3×C5×C19×C47 ⋊ C2
derived, HallC3×C19×C47 ⋊ C2×C5
HallC5×C19×C47 ⋊ D3
HallC19×C47 ⋊ C5×D3
HallC3×C5×C47 ⋊ D19
HallC3×C5×C19 ⋊ D47
HallC5×C47 ⋊ D57
HallC3×C47 ⋊ C5×D19
HallC5×C19 ⋊ D141
HallC3×C19 ⋊ C5×D47
SylowC47 ⋊ C5×D57
SylowC19 ⋊ C5×D141
HallC3×C5 ⋊ D893
SylowC3 ⋊ C5×D893

Subgroups

subgroupG/H
center, hypercenterC5D2679
commutator, cosocle, hypocenterC3×C19×C47C2×C5
FrattiniC1G
Fitting, socleC3×C5×C19×C47C2
LCSG ▷ C3×C19×C47
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13395

Conjugacy classes & character table

6705 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26790, 13);