Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(20,28,31,24)(21,33,34,25)(22,27)(23,26)(29,36,40,32)(30,39)(35,46,47,41)(37,38)(42,45)(43,48)(44,49);(18,20,23,31)(19,24,26,28)(21,30,34,45)(22,36,38,32)(25,39,33,42)(27,29,37,40)(35,48,47,44)(41,43,46,49);(18,19)(20,29)(21,25)(22,37)(23,26)(24,36)(27,38)(28,32)(30,43)(31,40)(33,34)(35,46)(39,48)(41,47)(42,44)(45,49);(18,21)(19,25)(20,30)(22,35)(23,34)(24,39)(26,33)(27,41)(28,42)(29,43)(31,45)(32,44)(36,48)(37,46)(38,47)(40,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17398);