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C11×D40 #11724909

order880
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D40

Splittings

FittingC5×C8×C11 ⋊ C2
HallC5×C11 ⋊ D8
SylowC5 ⋊ C11×D8

Subgroups

subgroupG/H
centerC2×C11D20
commutator, cosocleC4×C5C22×C11
FrattiniC4C2×D5×C11
FittingC5×C8×C11C2
socleC2×C5×C11D4
hypercenterC8×C11D5
hypocenterC5C11×D8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ C8×C11

44 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)(12,13,14,15,16,17,18,19)(20,21,22,23,24);(13,19)(14,18)(15,17)(21,24)(22,23)

Conjugacy classes & character table

253 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13182266, #13182268, #13182270, …
maximal normal subgroup of#13182266, #13182268, #13182270, …
maximal quotient ofC11×#3932, C11×D80, C11×Dic40, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 77);