Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#17972 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C23×C17 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C17×#431 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,26,22,25,31,33)(20,27,29,30,28,24,32,21)(34,35)(36,44)(37,41)(38,50)(39,42)(40,46)(43,52)(45,58)(47,57)(48,56)(49,62)(51,54)(53,60)(55,61)(59,65)(63,64);(18,20)(19,24)(21,26)(22,28)(23,29)(25,27)(30,33)(31,32)(34,36,39,47)(35,40,42,54)(37,45,48,59)(38,51,52,46)(41,53,56,64)(43,57,50,44)(49,63,61,60)(55,65,62,58);(18,21,23,27,22,30,31,24)(19,20,26,29,25,28,33,32)(34,37,39,48)(35,41,42,56)(36,45,47,59)(38,49,52,61)(40,53,54,64)(43,55,50,62)(44,58,57,65)(46,60,51,63);(19,25)(20,28)(26,33)(29,32)(35,42)(37,48)(40,54)(43,50)(44,57)(45,59)(49,61)(60,63)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10960);