Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1804 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
412 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)(20,30,33,47)(21,27)(22,26)(23,39)(24,29)(25,31,42,34)(28,37)(32,45,36,41)(35,43)(38,44)(40,49,46,48);(18,20)(19,25,29,42)(21,31)(22,36)(23,34)(24,33)(26,40,44,46)(27,30,39,47)(28,45,43,41)(32,38)(35,49)(37,48);(19,26)(21,23)(22,37)(25,40)(27,28)(29,44)(30,45)(31,34)(32,49)(35,38)(36,48)(39,43)(41,47)(42,46)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5814);