Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#17567 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C22×C22⋊C4 |
| prime radical | C2×C17×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×C42×C17 ◁ G | |
1046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(20,26,28,23)(21,25)(22,24)(27,32,33,30)(29,31)(34,35)(36,42,44,49)(37,41)(38,40)(39,43,47,45)(46,48);(18,20)(19,23)(21,27)(22,28)(24,26)(25,30)(29,33)(31,32)(34,36)(35,39)(37,45)(38,44)(40,47)(41,49)(42,48)(43,46);(19,24)(23,26)(25,31)(30,32)(35,40)(39,47)(41,48)(42,49);(18,21,22,29)(19,25,24,31)(20,27,28,33)(23,30,26,32)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10555);