Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #3958 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #357 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,5,3)(11,15)(12,19)(13,20)(16,17)(18,24)(21,25)(22,23);(2,3)(4,5)(6,7,8,9)(10,11)(12,15)(13,22)(14,18)(16,19)(17,20)(21,24)(23,25)Polycyclic presentation:
2^6,5|a^2=c,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^4,d^b=de,e^b=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | #10599971, #10599972, #10599973, … |
| maximal normal subgroup of | #10599971, #10599972, #10599973, … |
| maximal quotient of | #10598213, #10598254, #10598265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 120);