Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #3958 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #358 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,5,3)(10,11,14,17)(12,19,21,25)(13,22,20,16)(15,23,24,18);(2,3)(4,5)(6,7,8,9)(11,15)(12,18)(13,20)(16,25)(17,24)(19,22)(21,23)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,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 | #10600003, #10600004, #10600005, … |
| maximal normal subgroup of | #10600003, #10600004, #10600005, … |
| maximal quotient of | #10598213, #10598256, #10598267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 122);