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×#17680 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3515 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
878 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)(20,26,28,33)(21,25)(22,24)(23,27,31,29)(30,32)(34,35,39,42,40,36,38,44)(37,43,47,49,45,41,46,48);(18,20)(19,23)(21,29)(22,28)(24,31)(25,33)(26,32)(27,30)(34,36,40,35)(37,43,45,41)(38,42,39,44)(46,48,47,49);(19,24)(23,31)(25,32)(26,33)(34,37)(35,41)(36,43)(38,46)(39,47)(40,45)(42,48)(44,49);(37,45)(41,43)(46,47)(48,49)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10668);