Finite Group Databasebeta

← Prev (#11724903) Next (#11724905) →

C5×#4326 #11724904

order880
isoclinismisoclinic class of #4323
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#4326

Splittings

HallC5×C11 ⋊ Q16
SylowC11 ⋊ C5×Q16

Subgroups

subgroupG/H
centerC2×C5C22⋊D11
commutator, cosocleC4×C11C22×C5
FrattiniC4C2×C5×D11
FittingC5×Q8×C11C2
socle, prime radicalC2×C5×C11D4
hypercenterC5×Q8D11
hypocenterC11C5×Q16
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×Q8

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 880

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5)(6,7,9,11,13,15,16,14,12,10,8)(17,19,21,27)(18,22,24,31)(20,29,30,26)(23,32,28,25);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,21,24)(19,25,27,32)(20,28,30,23)(22,29,31,26)

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#4326, #13182927, #13182928, …
maximal normal subgroup ofD5×#4326, #13182927, #13182928, …
maximal quotient ofC5×#66871, C5×#66874, C5×#66899, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 72);