Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#2950 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D4 |
| commutator | C4 | C23×C4×C7 |
| Frattini, cosocle | C2×C4 | C24×C7 |
| prime radical | C23×C7 | C2×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#117 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13)(14,22)(15,19)(16,28)(17,20)(18,24)(21,30)(23,36)(25,35)(26,34)(27,40)(29,32)(31,38)(33,39)(37,43)(41,42);(12,14,17,25)(13,18,20,32)(15,23,26,37)(16,29,30,24)(19,31,34,42)(21,35,28,22)(27,41,39,38)(33,43,40,36);(8,10,11,9)(12,15,17,26)(13,19,20,34)(14,23,25,37)(16,27,30,39)(18,31,32,42)(21,33,28,40)(22,36,35,43)(24,38,29,41);(13,20)(15,26)(18,32)(21,28)(22,35)(23,37)(27,39)(38,41)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17025);