Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17409 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#121 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×Q8×C17 ◁ G | |
912 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(18,19,21,25,22,24,28,31)(20,23,27,30,26,29,32,33)(34,35,39,42,40,43,38,47)(36,44,45,48,37,41,46,49);(18,20)(19,23)(21,27)(22,26)(24,29)(25,30)(28,32)(31,33)(34,36)(35,41)(37,40)(38,45)(39,46)(42,48)(43,44)(47,49);(20,26)(23,29)(27,32)(30,33)(34,37,40,36)(35,41,43,44)(38,45,39,46)(42,49,47,48);(19,24)(23,29)(25,31)(30,33)(34,38,40,39)(35,42,43,47)(36,45,37,46)(41,48,44,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10397);