Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#18021 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C2×#41×C17 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C17×#431 ◁ G | |
592 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)(20,28)(21,26)(22,32)(23,27)(24,29)(25,30)(31,33)(34,35,37,40,38,41,44,47)(36,39,43,46,42,45,48,49);(18,20)(19,24)(21,29)(22,31)(23,30)(25,26)(27,33)(28,32);(18,20)(19,25)(21,31)(22,29)(23,30)(24,26)(27,28)(32,33)(34,36,37,43,38,42,44,48)(35,39,40,46,41,45,47,49);(18,21,23,22)(19,26,27,32)(20,29,30,31)(24,25,33,28)(36,42)(39,45)(43,48)(46,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11009);