Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #479 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,4,5,3)(6,9,10,7)(8,11,12,13)(15,20)(17,25)(19,26)(21,22)(23,29)(27,28);(6,8,10,12)(7,11,9,13)(14,16,18,24)(15,19,22,28)(17,23,25,29)(20,26,21,27);(2,3)(4,5)(6,7,10,9)(8,11,12,13)(14,15)(16,19)(17,20)(18,22)(21,25)(23,26)(24,28)(27,29)Polycyclic presentation:
2^6,5|a^2=e,b^2=ef,c^2=e,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce,d^c=df47 conjugacy classes — view the full character table.
| maximal subgroup of | #10612871, #10612873, #10612875, … |
| maximal normal subgroup of | #10612871, #10612873, #10612875, … |
| maximal quotient of | #10600333, #10600335, #10600352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 690);