Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#13211 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23)(24,32,35,45)(25,37)(26,29)(27,41)(28,34,42,38)(30,33)(31,40)(36,51,50,46)(39,52)(43,47,53,49)(44,48);(22,24,33,47,40,50,25,38,26,35,48,49,27,36,39,34)(23,28,37,51,41,53,30,45,29,42,52,46,31,43,44,32);(18,19,20,21)(23,29)(28,42)(30,44)(31,41)(32,45)(37,52)(43,53)(46,51)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6199);