Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#117 ⋊ C2 |
| Sylow | C5 ⋊ #421 |
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(7,12,13,14)(8,15)(11,18,19,20)(16,21);(6,8)(7,11)(9,16)(10,15)(12,20)(13,19)(14,18)(17,21);(2,3)(4,5)(6,7)(8,11)(9,12)(10,13)(14,17)(15,19)(16,20)(18,21)Polycyclic presentation:
2^6,5|c^2=d,e^2=f,c^a=ce,d^a=df,e^a=ef,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599493, #10599496, #10599497, … |
| maximal normal subgroup of | #10599493, #10599496, #10599497, … |
| maximal quotient of | #10600223, #10600233, #10600234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 632);