Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17521 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C22×C22⋊C4 |
| prime radical | C17×#3481 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C4×#41×C17 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(21,23)(22,26)(24,28)(25,30)(29,32)(31,33)(34,35,38,42,39,41,37,46)(36,43,44,40,45,49,47,48);(19,23)(21,30)(24,31)(25,26)(27,32)(29,33)(34,36)(35,40)(37,47)(38,44)(39,45)(41,48)(42,49)(43,46);(18,20)(19,24)(21,29)(22,28)(23,31)(25,32)(26,27)(30,33)(35,41)(40,48)(42,46)(43,49);(20,28)(24,27)(29,33)(31,32)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10509);