Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic150 |
| Hall | C3×C25 ⋊ Q8 |
| Sylow | C25 ⋊ Dic6 |
| Sylow | C3 ⋊ Dic50 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 600 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,2,3,4)(5,8,7,6)(9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36);(1,5,3,7)(2,6,4,8)(10,11)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)Polycyclic presentation:
2^3,3,5^2|a^2=c,b^2=c,e^5=f,b^a=bc,d^a=d^2,e^a=e^4f^4,f^a=f^4153 conjugacy classes — view the full character table.
| maximal subgroup of | #11924801, #11924804, #11924810, … |
| maximal normal subgroup of | #11924801, #11924804, #11924810, … |
| maximal quotient of | #11924863, C4⋊Dic75, C2×Dic150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 25);