Finite Group Databasebeta

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C11×#685 #11724916

order880
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C22

Aliases

direct productC11×#685

Splittings

FittingC2×C4×C5×C11 ⋊ C2
HallC5×C11 ⋊ C22⋊C4
SylowC5 ⋊ C11×C22⋊C4

Subgroups

subgroupG/H
centerC22×C11C2×D5
commutatorC2×C5C2×C4×C11
FrattiniC22C2×D5×C11
FittingC2×C4×C5×C11C2
socleC22×C5×C11C22
prime radicalC22×D5×C11C2
cosocleC22×C5C22×C11
hypercenterC2×C4×C11D5
hypocenterC5C11×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C11 ◁ C2×C4×C11

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of#13182709, #13182711, #13182729, …
maximal normal subgroup of#13182709, #13182711, #13182729, …
maximal quotient ofC11×#3937, C11×#3938, C11×#3941, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 84);