Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C4 |
| direct product | #491×C73 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C73 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ G | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 97 points:
(1,2)(3,6)(4,5)(7,8)(9,10,15,20)(11,17,22,23)(12,16,21,24)(13,19,14,18)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(2,5)(6,8)(9,11,13,12,15,22,14,21)(10,16,18,17,20,24,19,23);(1,3,4,7)(2,6,5,8)(9,12,13,22,15,21,14,11)(10,17,18,24,20,23,19,16)1168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 172);