Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64868 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #328 |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(6,8,9,13)(7,10,11,12)(14,15,17,19)(16,21,20,18);(2,3,4,5)(6,7)(8,12,13,10)(9,11)(15,18)(16,20)(19,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=e,d^2=ef,b^a=bd,d^a=de,g^a=g^2,c^b=cf,d^b=def,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#64869, #10604259, #10604261, … |
| maximal normal subgroup of | C2×#64869, #10604259, #10604261, … |
| maximal quotient of | #10598497, #10598498, #10598501, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 207);