Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#103 ⋊ C2 |
| Sylow | C5 ⋊ #467 |
114 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 41 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)(6,7)(8,9)(10,13,15,12)(11,16,18,20)(14,19,21,22)(17,24,25,23);(7,9)(10,12,14,19,15,13,21,22)(11,16,17,23,18,20,25,24);(2,3)(4,5)(7,9)(10,11)(12,16)(13,20)(14,17)(15,18)(19,23)(21,25)(22,24)Polycyclic presentation:
2^6,5|b^2=d,c^2=f,d^2=f,e^2=f,c^a=cde,g^a=g^4,c^b=cef,d^c=df,e^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65102, #10610531, #10610537, … |
| maximal normal subgroup of | C2×#65102, #10610531, #10610537, … |
| maximal quotient of | #10599234, #10599240, #10599258, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 440);