Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#13236 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C2×D8 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
438 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,24,25)(26,27)(28,39)(29,45)(30,48)(31,49)(32,38)(33,41)(34,42)(35,47)(36,40)(37,46)(43,57)(44,50)(51,54)(52,56)(53,55);(18,19,20,21)(23,25)(26,28,40,54,31,43,29,41,32,44,47,56,46,55,30,42)(27,33,48,57,37,51,35,39,38,34,45,53,49,52,36,50);(26,28,40,54,31,43,29,41,32,44,47,56,46,55,30,42)(27,34,48,53,37,52,35,50,38,33,45,57,49,51,36,39)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6224);