Finite Group Databasebeta

← Prev (#45686605) Next (#45686607) →

C13×AGL(1,𝔽7)×C61 #45686606

order33306
automorphism?
homologyAbelianization (H1) = C2×C3×C13×C61 · Schur multiplier (H2) = C1

Aliases

direct productC13×AGL(1,𝔽7)×C61
unambiguous semidirect productD7⋊(C3×C13×C61)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C13×C61)

Splittings

Fitting, socle, HallC7×C13×C61 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C13×C61
HallC13×ΓL(1,𝔽8)×C61 ⋊ C2
HallC13×D7×C61 ⋊ C3
HallΓL(1,𝔽8)×C61 ⋊ C2×C13
HallD7×C61 ⋊ C3×C13
HallC7×C61 ⋊ C2×C3×C13
HallC13×ΓL(1,𝔽8) ⋊ C2×C61
HallC13×D7 ⋊ C3×C61
HallC7×C13 ⋊ C2×C3×C61
HallΓL(1,𝔽8) ⋊ C2×C13×C61
HallD7 ⋊ C3×C13×C61

Subgroups

subgroupG/H
center, hypercenterC13×C61AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C13×C61
FrattiniC1G
Fitting, socleC7×C13×C61C2×C3
LCSG ▷ C7
UCSC1 ◁ C13×C61

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5551

Conjugacy classes & character table

5551 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33306, 73);