Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61856 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#540 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1612 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33)(34,35)(36,44)(37,48)(38,42)(39,52)(40,46)(41,50)(43,51)(45,60)(47,55)(49,57)(53,56)(54,64)(58,62)(59,63)(61,65);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36,38,46)(35,40,42,44)(37,45,49,61)(39,47,51,63)(41,54,56,58)(43,55,52,59)(48,65,57,60)(50,62,53,64);(34,37,38,49)(35,41,42,56)(36,45,46,61)(39,53,51,50)(40,54,44,58)(43,57,52,48)(47,64,63,62)(55,60,59,65);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(36,46)(40,44)(45,61)(47,63)(54,58)(55,59)(60,65)(62,64);(19,25)(23,26)(24,33)(31,32)(35,42)(36,46)(41,56)(43,52)(45,61)(47,63)(48,57)(62,64)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54844);