Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#7178 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #102 |
| commutator | C8 | C4×C8×C17 |
| Frattini, cosocle | C2×C4×C8 | C22×C17 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
274 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,25,28,26,29,24,27)(31,36,37,40)(32,33)(34,42)(38,45,44,39)(41,43);(19,21)(23,27,29,28)(30,31,33,38,42,45,32,40,35,37,43,44,34,39,41,36)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 166);