Finite Group Databasebeta

← Prev (#13183418) Next (#13183420) →

C5×#67040 #13183419

order1760
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#67040

Splittings

FittingC2×C5×Q8×C11 ⋊ C2
HallC5×C11 ⋊ 2−1+4
SylowC11 ⋊ C5×2−1+4

Subgroups

subgroupG/H
centerC2×C5C23×D11
commutator, cosocleC2×C11C24×C5
FrattiniC2C23×C5×D11
FittingC2×C5×Q8×C11C2
socleC2×C5×C11C24
hypercenterC2×C5×Q8D11
hypocenterC11C5×2−1+4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C5 ◁ C2×C5×Q8

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1228);