Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#12024 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D8 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C2×#107 |
| prime radical | C23×C17 | #107 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
226 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)(18,19,20,23,21,22,24,25)(26,27)(28,37)(29,34)(30,44)(31,46)(32,36)(33,40)(35,38)(39,50)(41,56)(42,52)(43,49)(45,57)(47,54)(48,55)(51,53);(26,28,38,53,31,41,45,55,32,42,43,54,29,39,30,40)(27,33,44,50,34,47,49,52,36,48,57,56,46,51,35,37);(19,22)(23,25)(26,29,32,31)(27,34,36,46)(28,39,42,41)(30,43,45,38)(33,47,48,51)(35,44,49,57)(37,50,52,56)(40,54,55,53)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5012);