Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C5×#103 ⋊ C2 |
| Sylow | C5 ⋊ #488 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,4,5,3)(7,11)(10,12)(14,16,18,24)(15,20,19,22)(17,26,25,23)(21,28,27,29);(6,8,9,13)(7,10,11,12)(15,19)(16,23)(17,25)(20,28)(22,29)(24,26);(2,3)(4,5)(6,7,9,11)(8,12,13,10)(14,15)(16,22)(17,21)(18,19)(20,24)(23,28)(25,27)(26,29)Polycyclic presentation:
2^6,5|a^2=e,b^2=e,c^2=f,d^2=f,b^a=bef,c^a=cef,g^a=g^4,c^b=cd,d^b=df,d^c=df50 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65089, #10610516, #10610538, … |
| maximal normal subgroup of | C2×#65089, #10610516, #10610538, … |
| maximal quotient of | #10599597, #10599637, #10599639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 427);