Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61111 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
2600 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(20,29)(21,33)(22,26)(23,40)(24,27)(25,32)(28,41)(30,47)(31,35)(34,36)(37,46)(38,45)(39,44)(42,49)(43,48);(18,20)(19,25)(21,27)(22,36)(23,33)(24,31)(26,43)(28,35)(29,40)(30,37)(32,41)(34,46)(38,48)(39,49)(42,45)(44,47);(18,21,24,25)(19,20,27,31)(22,34,39,42)(23,35,41,29)(26,30,44,48)(28,32,40,33)(36,46,49,45)(37,47,38,43);(18,22)(19,26)(20,30)(21,34)(23,38)(24,39)(25,42)(27,44)(28,46)(29,47)(31,48)(32,49)(33,36)(35,43)(37,41)(40,45);(19,27)(20,31)(26,44)(28,40)(30,48)(32,33)(36,49)(45,46)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54099);