Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #451 |
148 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)(10,12,19,23,14,21,13,20)(11,15,22,25,17,24,16,18);(6,7)(8,9);(2,3)(4,5)(10,11,14,17)(12,18,21,25)(13,22,19,16)(15,23,24,20)Polycyclic presentation:
2^6,5|a^2=f,c^2=df,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce59 conjugacy classes — view the full character table.
| maximal subgroup of | #10598902, #10598908, #10598925, … |
| maximal normal subgroup of | #10598902, #10598908, #10598925, … |
| maximal quotient of | #10598908, #10598910, #10598932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 366);