Finite Group DatabasebetaFinite Group Databasebeta| order | 12393 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C92×C17 · Schur multiplier (H2) = C35 |
| direct product | C3×C17×#6855 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C34×C17 | C32 |
| commutator | C3 | C3×C92×C17 |
| Frattini, cosocle | C33 | C33×C17 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C34×C17 ◁ G | |
1052 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 12393 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(4,5,7,6,8,10,9,11,12)(22,23,25)(24,27,29)(26,30,28);(13,14,16,15,17,19,18,20,21)(23,26,27)(25,29,30)5049 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12393, 103);