Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12778 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12780 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1790 |
| commutator | C2×Q8 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#3551 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×#41×C17 ◁ G | |
756 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)(21,34,22,27)(23,28)(24,29)(25,31,42,36)(26,35,43,37)(32,46)(33,44)(38,40)(39,45)(41,47,49,48);(18,20)(19,25)(21,31)(22,36)(23,38)(24,33)(26,40)(27,44)(28,41)(29,42)(30,34)(32,39)(35,48)(37,47)(43,46)(45,49);(18,21,24,22)(19,26,29,43)(20,31,33,36)(23,37,39,35)(25,40,42,46)(27,45,34,28)(30,41,44,49)(32,48,38,47)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5768);