Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C5×C8 ⋊ C4 |
| Sylow | C5 ⋊ #405 |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,5,4)(6,8,9,14,10,15,16,20)(7,12,13,19,11,17,18,21);(7,11)(12,17)(13,18)(19,21);(2,3,4,5)(6,7)(8,12)(9,13)(10,11)(14,19)(15,17)(16,18)(20,21)Polycyclic presentation:
2^6,5|a^2=d,c^2=e,e^2=f,b^a=bf,g^a=g^2,g^d=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #10598661, #10598662, #10598672, … |
| maximal normal subgroup of | #10598661, #10598662, #10598672, … |
| maximal quotient of | C8×#700, #10603809, #10603810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1056);