Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#11406 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C42 |
| commutator | C4 | C2×C4×C8×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C2×#97 |
| prime radical | C23×C17 | #97 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ G | |
282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(26,27,29,34,30,35,41,50,31,33,42,47,43,48,56,57)(28,36,38,51,39,46,54,49,37,52,40,55,53,32,44,45);(18,19,20,22,21,23,24,25)(26,28)(27,32,33,46)(29,40)(30,39)(31,37)(34,49,47,45)(35,36,48,52)(38,42)(41,44)(43,53)(50,55,57,51)(54,56);(27,33)(28,37)(34,47)(35,48)(38,40)(39,53)(44,54)(50,57)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4394);