Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#62154 |
| 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 ◁ C4×#41×C17 ◁ G | |
1720 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)(34,35,38,42)(36,43,39,40)(37,45,46,49)(41,47,48,44);(18,20)(19,23)(21,28)(22,27)(24,31)(25,26)(29,32)(30,33)(34,36,38,39)(35,40,42,43)(37,44,46,47)(41,45,48,49);(34,37,38,46)(35,41,42,48)(36,44,39,47)(40,45,43,49);(20,27)(23,26)(28,33)(31,32)(35,42)(40,43)(41,48)(45,49);(18,21,22,30)(19,24,25,29)(20,28,27,33)(23,31,26,32)(35,42)(40,43)(41,48)(45,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55142);