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)(6,8,18,34,11,21,25,35,12,22,23,27,9,19,10,20)(7,13,24,31,14,28,30,33,16,29,37,36,26,32,15,17);(2,3,4,5)(6,7,9,14,12,16,11,26)(8,17,19,31,22,33,21,36)(10,24,23,30,25,37,18,15)(13,27,28,35,29,34,32,20)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598493, #10598494, #10598680, … |
| maximal normal subgroup of | #10598493, #10598494, #10598680, … |
| maximal quotient of | #10598644, #10598647, #10598667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 189);