Finite Group Databasebeta

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C11×#709 #11725021

order880
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C23×C11 · Schur multiplier (H2) = C22

Aliases

direct productC11×#709

Splittings

FittingC2×C4×C5×C11 ⋊ C2
HallC5×C11 ⋊ #41
SylowC5 ⋊ C11×#41

Subgroups

subgroupG/H
centerC4×C11C2×D5
commutator, cosocleC2×C5C23×C11
FrattiniC2C22×D5×C11
FittingC2×C4×C5×C11C2
socleC2×C5×C11C23
hypercenterC2×C4×C11D5
hypocenterC5C11×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C11 ◁ C2×C4×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 440

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of#13182307, #13182308, C11×#3937, …
maximal normal subgroup of#13182307, #13182308, C11×#3937, …
maximal quotient ofC4×C11×Dic10, C11×#4016, C11×#4018, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 189);