Finite Group Databasebeta

← Prev (#39907639) Next (#39907641) →

C3⋊((C11⋊C5)⋊D79) #39907640

order26070
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊D79)
unambiguous semidirect product(C11⋊C5)⋊D237
unambiguous semidirect productC79⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect productD2607⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C79 ⋊ C2×C5
HallC3×C11⋊C5×C79 ⋊ C2
HallD2607 ⋊ C5
HallC11⋊C5×C79 ⋊ D3
HallC11×C79 ⋊ C5×D3
HallC3×C79 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ D79
SylowC79 ⋊ C3⋊AGL(1,𝔽11)
HallC11⋊C5 ⋊ D237
HallC3×C11 ⋊ C5×D79
SylowC11 ⋊ C5×D237
SylowC3 ⋊ (C11⋊C5)⋊D79

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C79C2×C5
LCSG ▷ C3×C11×C79
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2607

Polycyclic presentation:

2,3,5,11,79|b^a=b^2,d^a=d^10,e^a=e^78,d^c=d^4

Conjugacy classes & character table

837 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26070, 26);