Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #360 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,7)(8,15)(9,18)(10,12)(11,19)(13,17)(14,20)(16,21);(2,3)(4,5)(7,11,12,20)(8,14)(9,17)(13,15,18,21)(16,19)Polycyclic presentation:
2^6,5|a^2=c,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^4,c^b=cf,d^b=def,e^b=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10600039, #10600040, D5×#360, … |
| maximal normal subgroup of | #10600039, #10600040, D5×#360, … |
| maximal quotient of | #10598217, #10598253, #10598255, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 124);