Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#13104 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C17 | C23 |
| commutator | C22 | C22×C16×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle, prime radical | C23×C17 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C17 ◁ G | |
326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,27)(25,26)(28,29)(30,31,35,40,36,32,41,42,34,39,43,45,33,38,37,44);(23,26)(27,29)(30,32,35,42,36,39,41,45,34,38,43,44,33,31,37,40);(19,21)(22,24,25,28)(23,27,26,29)(30,33,34,36)(31,38,39,32)(35,37,43,41)(40,44,45,42)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6092);