Finite Group Databasebeta

← Prev (#13183088) Next (#13183090) →

C11×#4022 #13183089

order1760
automorphism?
homologyAbelianization (H1) = C23×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×#4022

Splittings

FittingC42×C5×C11 ⋊ C2
HallC5×C11 ⋊ #126
SylowC5 ⋊ C11×#126

Subgroups

subgroupG/H
centerC22×C11C22×D5
commutator, cosocleC22×C5C23×C11
FrattiniC22C22×D5×C11
FittingC42×C5×C11C2
socleC22×C5×C11C23
prime radicalC22×D5×C11C22
hypercenterC42×C11D5
hypocenterC5C11×#126
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C11 ◁ C42×C11

120 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)(18,22)(21,24)(25,27,28,32)(26,30,29,31);(17,19,20,23)(18,21,22,24)(26,29)(30,31);(13,14)(15,16)(17,18)(19,21)(20,22)(23,24)(25,26)(27,31)(28,29)(30,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 898);