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C11×#713 #11725025

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

Aliases

direct productC11×#713

Splittings

FittingC5×Q8×C11 ⋊ C2
HallC5×C11 ⋊ #41
SylowC5 ⋊ C11×#41

Subgroups

subgroupG/H
centerC2×C11C22×D5
commutator, cosocleC2×C5C23×C11
FrattiniC2C22×D5×C11
FittingC5×Q8×C11C2
socleC2×C5×C11C23
hypercenterQ8×C11D5
hypocenterC5C11×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ Q8×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)(17,19,20,23)(18,21,22,24);(17,18,20,22)(19,24,23,21);(13,14)(15,16)(19,23)(21,24)

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×#4010, #13182655, #13182921, …
maximal normal subgroup ofC11×#4010, #13182655, #13182921, …
maximal quotient ofC11×#4036, C11×#4038, C11×#4039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 193);