Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#359 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | D8 |
| commutator | C8 | C2×C4×C23 |
| Frattini, cosocle | C2×C8 | C22×C23 |
| socle | C2×C23 | #102 |
| prime radical | C23×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C2×C4×C23 ◁ C2×C8×C23 ◁ G | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 2 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,33,30,34,29,44)(26,35,37,51,38,52,45,49)(27,39,41,50,43,54,42,32)(31,40,46,53,48,55,47,36);(24,26)(25,31)(27,40)(28,37)(29,45)(30,38)(32,49)(33,46)(34,48)(35,39)(36,42)(41,53)(43,55)(44,47)(50,51)(52,54)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 40);