Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36912 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
1570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(20,24)(23,25)(27,31)(29,32)(34,35,40,39)(36,43,38,41)(37,45,47,42)(44,48,46,49);(19,22)(23,25)(27,31)(28,33)(34,36,40,38)(35,41,39,43)(37,46,47,44)(42,49,45,48);(18,19)(20,23)(21,22)(24,25)(26,27,30,31)(28,32,33,29)(34,37,40,47)(35,42,39,45)(36,44,38,46)(41,48,43,49);(18,19)(20,23)(21,22)(24,25)(26,28)(27,32)(29,31)(30,33)(34,38,40,36)(35,43,39,41)(37,46,47,44)(42,49,45,48);(18,20)(19,23)(21,24)(22,25)(26,29,30,32)(27,28,31,33)(34,39,40,35)(36,43,38,41)(37,45,47,42)(44,49,46,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29900);