Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#11924 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C2×#102 |
| prime radical | C17×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
414 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)(28,38,41,54)(29,34)(30,44)(31,36)(32,37)(33,40,49,57)(35,46)(39,51,42,55)(43,53)(45,48,56,50)(47,52);(19,22)(20,24)(26,28)(27,33)(29,39)(30,45)(31,42)(32,41)(34,48)(35,51)(36,50)(37,49)(38,52)(40,43)(44,54)(46,57)(47,56)(53,55);(26,29,32,31)(27,34,37,36)(28,39,41,42)(30,43,47,46)(33,48,49,50)(35,44,53,52)(38,51,54,55)(40,56,57,45)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4912);