Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #427 |
114 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)(10,13,14,21,15,22,12,19)(11,17,16,20,18,24,23,25);(10,12,15,14)(11,16,18,23)(13,19,22,21)(17,20,24,25);(2,3)(4,5)(6,7,8,9)(10,11)(12,16)(13,20)(14,23)(15,18)(17,21)(19,24)(22,25)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^492 conjugacy classes — view the full character table.
| maximal subgroup of | #10598212, #10598216, #10598220, … |
| maximal normal subgroup of | #10598212, #10598216, #10598220, … |
| maximal quotient of | #10600522, #10600525, C4×#3949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 733);