Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ #452 |
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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)(10,12,14,19)(11,16,15,22)(13,21,20,18)(17,24,23,25);(11,15)(12,18)(13,20)(16,24)(19,21)(22,25);(2,3)(4,5)(6,7)(8,9)(10,11)(12,16)(13,17)(14,15)(18,25)(19,22)(20,23)(21,24)Polycyclic presentation:
2^6,5|c^2=f,e^2=f,b^a=bf,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 | #10611383, #10611386, #10611388, … |
| maximal normal subgroup of | #10611383, #10611386, #10611388, … |
| maximal quotient of | #10600960, #10600992, #10600999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 800);