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×#11709 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×#102 |
| prime radical | C17×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
450 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)(20,24,25,22)(21,23)(26,27,29,34,32,37,31,36)(28,38,41,52,42,55,39,54)(30,44,43,35,47,51,46,53)(33,45,49,40,50,56,48,57);(18,20)(19,22)(21,25)(23,24)(26,28)(27,33)(29,39)(30,45)(31,41)(32,42)(34,48)(35,52)(36,49)(37,50)(38,51)(40,46)(43,57)(44,55)(47,56)(53,54);(26,29,32,31)(27,34,37,36)(28,39,42,41)(30,43,47,46)(33,48,50,49)(35,51,53,44)(38,54,55,52)(40,45,57,56)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4697);