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C5×#4343 #11725015

order880
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#4343

Splittings

FittingC5×Q8×C11 ⋊ C2
HallC5×C11 ⋊ #41
SylowC11 ⋊ C5×#41

Subgroups

subgroupG/H
centerC2×C5C22×D11
commutator, cosocleC2×C11C23×C5
FrattiniC2C22×C5×D11
FittingC5×Q8×C11C2
socleC2×C5×C11C23
hypercenterC5×Q8D11
hypocenterC11C5×#41
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C5 ◁ C5×Q8

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

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13182919, #13182925, #13182931, …
maximal normal subgroup of#13182919, #13182925, #13182931, …
maximal quotient ofC5×#66943, C5×#66945, C5×#66946, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 183);