Finite Group Databasebeta

← Prev (#13183119) Next (#13183121) →

C11×#4053 #13183120

order1760
automorphism?
homologyAbelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22

Aliases

direct productC11×#4053

Splittings

FittingC5×C11×M16 ⋊ C2
HallC5×C11 ⋊ #131
SylowC5 ⋊ C11×#131

Subgroups

subgroupG/H
centerC4×C11C22×D5
commutatorC2×C5C22×C4×C11
FrattiniC4C22×D5×C11
FittingC5×C11×M16C2
socleC2×C5×C11C22×C4
prime radicalC11×#709C2
cosocleC4×C5C23×C11
hypercenterC11×M16D5
hypocenterC5C11×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C11 ◁ C11×M16

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 880

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16,14)(17,19,20,26,21,25,27,31)(18,23,24,30,22,28,29,32);(18,22)(19,25)(24,29)(26,31);(13,14)(15,16)(17,18)(19,23)(20,24)(21,22)(25,28)(26,30)(27,29)(31,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 929);