Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17684 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3517 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
932 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,28,24,27,22,26)(20,29,30,33,21,25,31,32)(34,35)(36,42,44,49)(37,41)(38,40)(39,43,47,45)(46,48);(18,20,24,21)(19,25,27,29)(22,30,23,31)(26,32,28,33)(34,36)(35,39)(37,45)(38,44)(40,47)(41,49)(42,48)(43,46);(18,21,24,20)(19,25,27,29)(22,30,23,31)(26,33,28,32)(35,40)(39,47)(41,48)(42,49);(18,22,24,23)(19,26,27,28)(20,30,21,31)(25,32,29,33)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10672);