Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#19613 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×#127 |
| prime radical | C17×#3169 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,27)(21,25)(22,31)(23,26)(24,30)(28,33)(29,32)(34,35)(36,42)(37,39)(38,46)(40,44)(41,45)(43,48)(47,49);(18,20,22,30,23,28,21,29)(19,24,25,27,26,32,31,33)(35,39)(40,47)(41,46)(42,48);(20,28)(24,32)(27,33)(29,30)(34,36,38,44,37,43,45,49)(35,40,41,42,39,47,46,48);(18,21,23,22)(19,25,26,31)(20,29,28,30)(24,27,32,33)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12601);