Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#100 ⋊ C2 |
| Sylow | C5 ⋊ #413 |
150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,8,9,15,10,14,16,20)(7,12,13,19,11,17,18,21);(7,11)(8,14)(9,16)(19,21);(2,3)(4,5)(6,7)(8,12)(9,13)(10,11)(14,17)(15,19)(16,18)(20,21)Polycyclic presentation:
2^6,5|c^2=d,d^2=f,b^a=bf,g^a=g^4,c^b=ce,d^b=df,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10598574, #10599929, #10599930, … |
| maximal normal subgroup of | #10598574, #10599929, #10599930, … |
| maximal quotient of | #10598893, #10598895, #10598898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 372);