Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#11893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(20,24,25,22)(21,23)(26,27,30,36,32,38,31,37)(28,39,42,55,44,56,43,53)(29,45,47,35,49,54,48,34)(33,46,50,41,52,57,51,40);(18,20)(19,22)(21,25)(23,24)(26,28)(27,33)(29,46)(30,43)(31,42)(32,44)(34,53)(35,55)(36,51)(37,50)(38,52)(39,54)(40,47)(41,48)(45,56)(49,57);(20,25)(22,24)(26,29,30,47,32,49,31,48)(27,34,37,54,38,35,36,45)(28,40,42,46,44,41,43,57)(33,39,51,53,52,56,50,55)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4881);