Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64849 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #368 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,5,4)(6,8,18,25,22,35,10,20,11,21,34,37,9,19,24,36)(7,12,26,32,13,27,14,17,16,29,23,31,15,28,30,33);(2,3,4,5)(6,7,9,13,11,16,22,15)(8,17,19,31,21,33,35,32)(10,23,18,30,24,26,34,14)(12,25,27,36,29,37,28,20)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^2,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598491, #10598492, #10598681, … |
| maximal normal subgroup of | #10598491, #10598492, #10598681, … |
| maximal quotient of | #10598645, #10598646, #10598667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 190);