Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #417 |
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(6,7,8,9)(11,16)(12,13)(15,17);(10,12,14,13)(11,15,17,16);(2,3)(4,5)(10,11)(12,15)(13,16)(14,17)Polycyclic presentation:
2^6,5|b^2=f,c^2=d,e^2=f,c^a=ce,e^a=ef,g^a=g^4,c^b=cf,e^c=ef62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599779, #10599780, #10599793, … |
| maximal normal subgroup of | #10599779, #10599780, #10599793, … |
| maximal quotient of | #10600191, #10600263, #10600267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 593);