Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#17824 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C22×C4⋊C4 |
| prime radical | C2×#41×C17 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C4×#41×C17 ◁ G | |
572 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)(19,23)(21,28)(24,29)(25,30)(27,32)(31,33)(34,35,37,41,38,40,44,47)(36,39,43,46,42,45,48,49);(18,19,21,23,22,25,28,30)(20,24,27,29,26,31,32,33)(34,36)(35,39)(37,43)(38,42)(40,45)(41,46)(44,48)(47,49);(18,20)(19,24)(21,27)(22,26)(23,29)(25,31)(28,32)(30,33)(36,42)(39,45)(43,48)(46,49);(20,26)(24,31)(27,32)(29,33)(35,40)(39,45)(41,47)(46,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10812);