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×#24408 |
| 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 | |
1364 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)(20,28,30,24)(21,25)(22,27)(23,26)(29,38,47,46)(31,44,35,39)(32,40,48,49)(33,42)(34,41)(36,45)(37,43);(18,20)(19,24)(21,32)(22,35)(23,30)(25,40)(26,28)(27,44)(29,34)(31,37)(33,48)(36,47)(38,41)(39,43)(42,49)(45,46);(18,21)(19,25)(20,29)(22,36)(23,33)(24,38)(26,42)(27,45)(28,46)(30,47)(31,48)(32,35)(34,37)(39,49)(40,44)(41,43);(18,20)(19,24)(21,29)(22,31)(23,30)(25,38)(26,28)(27,39)(32,34)(33,47)(35,37)(36,48)(40,41)(42,46)(43,44)(45,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17396);