Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#62157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#529 ◁ G | |
1684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,25)(20,26,27,23)(21,29,30,24)(28,31,33,32)(36,42)(37,44)(39,46)(41,48)(43,45)(47,49);(18,20)(19,23)(21,28)(22,27)(24,31)(25,26)(29,32)(30,33)(34,35)(36,39)(37,41)(38,40)(42,46)(43,47)(44,48)(45,49);(34,36,38,43)(35,39,40,47)(37,45,44,42)(41,49,48,46);(20,27)(23,26)(28,33)(31,32);(18,21,22,30)(19,24,25,29)(20,28,27,33)(23,31,26,32)(35,40)(39,47)(41,48)(46,49)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55145);