Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#8781 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #117 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #382 |
| prime radical | C23×C17 | #117 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C17×#376 ◁ G | |
310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(18,19,21,23,20,22,24,25)(26,27)(28,36,39,32)(29,40,42,55)(30,35)(31,34)(33,41,46,56)(37,50)(38,49,53,45)(43,47)(44,51)(48,57)(52,54);(19,22)(23,25)(26,28,30,38,31,39,43,53)(27,32,35,45,34,36,47,49)(29,37,41,51,42,52,56,57)(33,44,40,54,46,48,55,50);(26,29)(27,33,34,46)(28,37)(30,41)(31,42)(32,44,36,48)(35,40,47,55)(38,51)(39,52)(43,56)(45,54,49,50)(53,57)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1769);