Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #491 |
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)(6,8,9,13)(7,11,10,12)(15,20)(16,23)(17,25)(19,26)(21,22)(27,28);(6,7,9,10)(8,12,13,11)(14,16)(15,19)(17,24)(18,23)(20,28)(21,26)(22,27)(25,29);(2,3)(4,5)(7,10)(11,12)(14,15,18,22)(16,19,23,27)(17,20,25,21)(24,28,29,26)Polycyclic presentation:
2^6,5|a^2=f,b^2=e,c^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=cef,d^c=df44 conjugacy classes — view the full character table.
| maximal subgroup of | #10598736, #10598737, #10598742, … |
| maximal normal subgroup of | #10598736, #10598737, #10598742, … |
| maximal quotient of | #10600341, #10600345, #10600353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 696);