Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C22 |
| direct product | #462×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 | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 93 points:
(2,4)(5,6,9,12)(7,13,15,20)(8,16,18,11)(10,17,19,14)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,2,3,4);(5,7,9,15)(6,10,12,19)(8,17,18,14)(11,20,16,13)1387 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 143);