Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#11648 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D8 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C2×#102 |
| prime radical | C17×#466 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,24,22,25,28,31)(20,23,27,30,26,29,32,33)(35,39)(36,42)(37,44)(40,47)(41,48)(43,46)(45,49);(18,20)(19,23)(21,27)(22,26)(24,30)(25,29)(28,32)(31,33)(34,35)(36,43)(37,46)(38,40)(39,42)(41,44)(45,48)(47,49);(20,26)(23,29)(27,32)(30,33)(35,40)(39,47)(41,46)(43,48)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4636);