Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #340 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(10,11,12,13)(14,15,16,18,17,19,20,21);(2,3)(4,5)(6,7,8,9)(15,18)(16,20)(19,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,d^2=f,b^a=bd,d^a=df,g^a=g^492 conjugacy classes — view the full character table.
| maximal subgroup of | #10598017, #10598019, #10598265, … |
| maximal normal subgroup of | #10598017, #10598019, #10598265, … |
| maximal quotient of | #10598145, #10598146, #10598166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 109);