Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #362 |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,4,5,3)(6,8,11,20)(7,12,16,29)(9,21,23,18)(10,25,26,35)(13,28,15,27)(14,31,32,33)(17,24,34,30)(19,22,36,37);(2,3)(4,5)(6,7,9,13,11,16,23,15)(8,17,18,31,20,34,21,33)(10,24,22,14,26,30,37,32)(12,25,27,19,29,35,28,36)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^4,c^b=cf,d^b=def,e^b=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#362, #10600059, #10600060, … |
| maximal normal subgroup of | D5×#362, #10600059, #10600060, … |
| maximal quotient of | #10598214, #10598255, #10598268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 123);