Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#11659 |
| 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×#102 |
| prime radical | C2×C17×#135 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
364 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)(30,42)(31,46)(32,36)(33,39)(35,44)(38,53)(40,54)(41,52)(43,48)(45,56)(47,51)(49,57)(50,55);(26,28)(27,33)(29,38)(30,43)(31,47)(32,40)(34,48)(35,51)(36,50)(37,42)(39,44)(41,55)(45,57)(46,49)(52,53)(54,56);(19,22)(23,25)(26,29,32,31)(27,34,36,46)(28,38,40,47)(30,41,45,44)(33,48,50,49)(35,42,52,56)(37,53,54,51)(39,43,55,57)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4647);