Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C73 · Schur multiplier (H2) = C2 |
| direct product | #355×C73 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | #99 |
| commutator | C2×C4 | C2×C4×C73 |
| Frattini, cosocle | C2×Q8 | C22×C73 |
| prime radical | C2×D4×C73 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C73 ◁ C2×Q8×C73 ◁ G | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 1168 |
A minimal faithful permutation representation — 2 generators on 89 points:
(1,2,4,8,5,9,13,16)(3,7,11,15,10,6,12,14)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(2,6)(3,10)(7,9)(8,15)(11,12)(14,16)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 36);