Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11389 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #391 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1446 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
836 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24,29,38)(21,31)(22,34)(23,26)(25,33)(27,35)(28,41,43,46)(30,45,44,37)(32,47)(36,49,39,42)(40,48);(18,20)(19,24,26,38)(21,28)(22,30)(23,29)(25,39,40,36)(27,37,34,45)(31,46,47,41)(32,43)(33,42)(35,44)(48,49);(18,21)(19,25,26,40)(20,28)(22,33)(23,32)(24,36,38,39)(27,31,34,47)(29,43)(30,42)(35,48)(37,41,45,46)(44,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4377);