Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #495 |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(7,9)(11,16)(12,19)(13,22)(15,23)(18,25)(20,21);(7,9)(10,12)(11,15)(13,19)(14,21)(16,18)(17,25)(20,22)(23,24);(2,3)(4,5)(6,7,8,9)(10,11)(12,18)(13,17)(14,16)(15,21)(19,23)(20,25)(22,24)Polycyclic presentation:
2^6,5|a^2=e,d^2=f,b^a=bef,c^a=cef,g^a=g^4,c^b=cd,d^b=df,d^c=df50 conjugacy classes — view the full character table.
| maximal subgroup of | #10598800, #10599977, #10599978, … |
| maximal normal subgroup of | #10598800, #10599977, #10599978, … |
| maximal quotient of | #10600951, #10600974, #10600982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 782);