Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#7258 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #102 |
| commutator | C2×C8 | C42×C17 |
| Frattini, cosocle | C23×C8 | C22×C17 |
| prime radical | C24×C17 | D8 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1088 |
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)(24,26)(25,28)(27,29)(30,31)(32,35)(33,42)(34,38)(36,39)(37,40)(41,44)(43,45);(23,26,28,27)(31,35)(32,39)(33,40)(36,37)(38,44)(41,45)(42,43)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 246);