Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#11594 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D8 |
| commutator | C8 | C22×C8×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C2×#102 |
| prime radical | C23×C17 | #102 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
386 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)(18,19,20,22,21,23,24,25)(26,27)(28,37)(29,34)(30,43)(31,47)(32,36)(33,39)(35,45)(38,51)(40,57)(41,54)(42,52)(44,50)(46,53)(48,55)(49,56);(26,28,32,41)(27,33,36,49)(29,40,31,38)(30,44,46,55)(34,50,47,48)(35,51,52,57)(37,53,54,43)(39,42,56,45);(26,29,32,31)(27,34,36,47)(28,38,41,40)(30,42,46,45)(33,48,49,50)(35,43,52,53)(37,51,54,57)(39,55,56,44)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4582);