Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#441 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C23 | C2×D4 |
| commutator | C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C4 | C23×C23 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,26)(28,29)(30,36)(31,39)(32,34)(33,37)(35,41)(38,43)(40,42);(28,30,32,38)(29,33,34,42)(31,40,41,37)(35,43,39,36);(24,26,27,25)(29,34)(33,42)(35,39)(36,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 122);