Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17547 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17616 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×Q8×C17 ◁ G | |
918 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)(20,27)(21,25)(22,30)(23,26)(24,28)(29,32)(31,33)(35,39,41,44)(40,46,47,49);(18,20)(19,24)(21,28)(22,31)(23,29)(25,32)(26,33)(27,30)(34,35)(36,40)(37,44)(38,41)(39,45)(42,47)(43,49)(46,48);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(34,36)(35,40)(37,43)(38,42)(39,46)(41,47)(44,49)(45,48);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(36,42)(40,47)(43,48)(46,49)1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10604);