Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ #451 |
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(7,9)(10,12,14,20)(11,15,17,24)(13,22,23,19)(16,25,21,18);(10,11,14,17)(12,18,20,25)(13,21,23,16)(15,22,24,19);(2,3)(4,5)(6,7)(8,9)Polycyclic presentation:
2^6,5|b^2=f,c^2=f,e^2=f,c^a=cd,g^a=g^4,c^b=ce,e^b=ef,e^c=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | #10611453, #10611454, #10611455, … |
| maximal normal subgroup of | #10611453, #10611454, #10611455, … |
| maximal quotient of | #10601024, #10601028, #10601059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 813);