Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12948 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1864 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
384 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,25,28,27)(20,30,31,48)(21,33)(22,37)(23,36)(26,43)(29,38,40,34)(32,39,41,35)(42,49)(44,46);(18,19,23,40,24,28,36,29)(20,26,41,45,31,43,32,47)(21,34,33,25,22,38,37,27)(30,42,39,49,48,46,35,44);(18,20)(19,26)(21,35)(22,39)(23,41)(24,31)(25,42)(27,46)(28,43)(29,47)(30,33)(32,36)(34,44)(37,48)(38,49)(40,45)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5936);