Finite Group Databasebeta

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C11×#4021 #13183088

order1760
automorphism?
homologyAbelianization (H1) = C23×C11 · Schur multiplier (H2) = C2×C4

Aliases

direct productC11×#4021

Splittings

FittingC42×C5×C11 ⋊ C2
HallC5×C11 ⋊ #124
SylowC5 ⋊ C11×#124

Subgroups

subgroupG/H
centerC22×C11C22×D5
commutator, cosocleC22×C5C23×C11
FrattiniC22C22×D5×C11
FittingC42×C5×C11C2
socleC22×C5×C11C23
prime radicalC2×C11×D20C2
hypercenterC42×C11D5
hypocenterC5C11×#124
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C11 ◁ C42×C11

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 880

A minimal faithful permutation representation — 3 generators on 28 points:

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

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, 897);