Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34336 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2024 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(23,26)(27,29)(30,31,36,34)(32,39,33,37)(35,42,43,38)(40,44,41,45);(30,32,36,33)(31,37,34,39)(35,40,43,41)(38,44,42,45);(22,23,25,26)(24,27,28,29)(30,33,36,32)(31,37,34,39)(35,41,43,40)(38,44,42,45);(30,34,36,31)(32,37,33,39)(35,42,43,38)(40,44,41,45);(18,20,21,19)(22,24,25,28)(23,27,26,29)(30,35,36,43)(31,38,34,42)(32,40,33,41)(37,44,39,45)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27324);