Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #494 |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(10,12,19,23,14,21,13,20)(11,15,22,25,17,24,16,18);(6,7,8,9);(2,3)(4,5)(7,9)(10,11,14,17)(12,18,21,25)(13,22,19,16)(15,23,24,20)Polycyclic presentation:
2^6,5|a^2=f,b^2=e,c^2=df,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^486 conjugacy classes — view the full character table.
| maximal subgroup of | #10597965, #10598052, #10598063, … |
| maximal normal subgroup of | #10597965, #10598052, #10598063, … |
| maximal quotient of | #10598856, #10598857, #10598858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 326);