Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#8135 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C17 | C23 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle, prime radical | C23×C17 | C2×C42 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C17 ◁ G | |
382 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)(18,19)(20,23)(21,22)(24,25)(26,27,29,33,30,32,36,39)(28,31,35,37,34,38,40,41)(42,43)(44,47)(45,49)(46,48)(50,54)(51,53)(52,55)(56,57);(19,22)(23,25)(26,28)(27,31)(29,35)(30,34)(32,38)(33,37)(36,40)(39,41)(42,44,45,50,46,51,52,56)(43,47,49,54,48,53,55,57);(18,20,21,24)(19,23,22,25)(27,32)(28,34)(33,39)(35,40)(43,48)(47,53)(49,55)(54,57)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1123);