Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42×C17 · Schur multiplier (H2) = C28×C4 |
| direct product | C17×#33999 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C2 | C23×C42×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| socle | C23×C17 | C25 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
3598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(26,27)(28,34)(29,33)(30,32)(31,35)(36,40)(37,39)(38,41);(22,23,24,25)(26,28)(27,31)(29,36)(30,35)(32,34)(33,38)(37,41)(39,40);(18,20,21,19)(28,35)(31,34)(36,41)(38,40);(27,32)(31,34)(33,39)(38,40);(26,29,30,37)(27,33,32,39)(28,36,35,41)(31,38,34,40)2312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26987);