Finite Group DatabasebetaFinite Group Databasebeta| order | 12393 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C17×C27 · Schur multiplier (H2) = C9 |
| direct product | C17×#10624443 |
| subgroup | G/H | |
|---|---|---|
| center | C92×C17 | C32 |
| commutator | C3 | C9×C17×C27 |
| Frattini, cosocle | C92 | C32×C17 |
| socle, prime radical | C32×C17 | C92 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C92×C17 ◁ G | |
116 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 12393 |
A minimal faithful permutation representation — 2 generators on 71 points:
(28,29,32,30,34,40,36,43,48,31,35,39,37,44,47,45,51,53,38,33,41,46,42,49,52,50,54)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71);(1,2,5,3,6,11,8,13,18,4,7,12,9,14,19,16,21,24,10,15,20,17,22,25,23,26,27)(29,33,35)(32,39,41)(34,42,44)(40,47,49)(43,50,51)(48,53,54)5049 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12393, 3);