Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12981 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #120 |
| commutator | C23 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1869 |
| prime radical | C17×#525 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,27,23,28,36,42,24,20,25,30,37,31,38,44)(21,29,33,41,34,43,46,49,32,26,35,39,45,40,47,48);(18,20,22,30,23,31,36,44,24,19,25,27,37,28,38,42)(21,29,35,39,34,43,47,48,32,26,33,41,45,40,46,49);(18,21)(19,26)(20,29)(22,35)(23,34)(24,32)(25,33)(27,41)(28,40)(30,39)(31,43)(36,47)(37,45)(38,46)(42,49)(44,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5969);