Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12740 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1786 |
| prime radical | C2×C17×#575 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C22×M16×C17 ◁ G | |
914 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,27,24,28,23,38)(20,29,32,46,31,45,39,43)(21,33,36,44,35,48,37,26)(25,34,41,47,40,49,42,30);(18,20)(19,25)(21,34)(22,32)(23,39)(24,31)(26,43)(27,41)(28,40)(29,33)(30,37)(35,49)(36,47)(38,42)(44,46)(45,48);(21,35)(26,44)(29,45)(30,47)(33,48)(34,49)(36,37)(43,46)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5728);