Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C42 |
| direct product | C7×#1747 |
| subgroup | G/H | |
|---|---|---|
| center | C7×C8 | C42 |
| commutator | C4 | C2×C42×C7 |
| Frattini, cosocle | C22×C4 | C23×C7 |
| socle | C2×C7 | #376 |
| prime radical | C23×C7 | #41 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C7×C8 ◁ G | |
200 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18,21,31)(11,15)(12,16)(13,17)(14,20,26,34)(19,30,33,38)(22,27)(23,28)(24,29)(25,32,36,39)(35,37);(8,10)(9,14,17,26)(11,19)(12,20)(13,21)(15,25,28,36)(16,18,29,31)(22,32)(23,33)(24,34)(27,30,37,38)(35,39);(8,11,12,22,13,23,24,35)(9,15,16,27,17,28,29,37)(10,19,20,32,21,33,34,39)(14,25,18,30,26,36,31,38)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4982);