Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11176 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #124 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #394 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
834 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,34,37,29)(25,38,41,49)(26,32)(27,33)(28,31)(30,40,47,43)(35,46)(36,48,42,45)(39,50)(44,51)(52,53);(22,24)(23,29)(25,39)(26,36)(27,42)(28,37)(30,46)(31,34)(32,45)(33,48)(35,40)(38,44)(41,51)(43,52)(47,53)(49,50);(19,21)(22,25)(23,30,31,47)(24,35)(26,40)(27,43)(28,41)(29,44,34,50)(32,38,33,49)(36,51)(37,52)(39,42)(45,53,48,46)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4164);