Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ #464 |
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 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)(7,9)(10,12,14,18)(11,15,17,24)(13,22,23,20)(16,25,21,19);(10,11,14,17)(12,19,18,25)(13,21,23,16)(15,22,24,20);(2,3)(4,5)(6,7,8,9)(12,18)(15,24)(19,25)(20,22)Polycyclic presentation:
2^6,5|a^2=e,b^2=f,c^2=f,d^2=f,c^a=cef,g^a=g^4,c^b=cd,d^b=df,d^c=df47 conjugacy classes — view the full character table.
| maximal subgroup of | #10611431, #10611432, #10611434, … |
| maximal normal subgroup of | #10611431, #10611432, #10611434, … |
| maximal quotient of | #10601015, #10601023, #10601027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 812);