Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C17 · Schur multiplier (H2) = C42 |
| direct product | C17×#12541 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C42 |
| commutator | C4 | C43×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×#97 |
| prime radical | C23×C17 | C2×M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,25,29,26,31,37,45,27,30,38,44,39,46,52,53)(24,32,34,48,35,41,50,43,33,47,36,51,49,28,40,42);(22,24)(23,28,30,41)(25,36)(26,35)(27,33)(29,43,44,42)(31,32,46,47)(34,38)(37,40)(39,49)(45,51,53,48)(50,52);(18,19,20,21)(24,33)(28,41)(32,47)(34,36)(35,49)(40,50)(42,43)(48,51)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5529);