Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C22×C42 |
| direct product | C17×#21644 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#127 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C17×#376 ◁ G | |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 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)(22,23)(24,27)(25,26)(28,29)(31,35)(32,38)(33,39)(36,43)(37,42)(40,44);(23,26)(27,29)(30,31,33,35,34,37,39,42)(32,36,38,41,40,43,44,45);(22,24,25,28)(23,27,26,29)(30,32,39,44,34,40,33,38)(31,36,42,45,37,43,35,41);(18,20,21,19)(31,37)(35,42)(36,43)(41,45)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14632);