Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C19 |
| abelian | C3×C4×C7×C192 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C2×C3×C7×C192 |
| socle, prime radical | C2×C3×C7×C192 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
264 conjugacy classes of subgroups.
| minimal degree | μ(G) = 52 |
| transitive degree | μt(G) = 30324 |
A minimal faithful permutation representation — 2 generators on 52 points:
(1,2,3,4)(5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)30324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 65);