Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#3256 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C7 |
| prime radical | C7×#469 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17)(18,25)(19,23)(20,22)(21,26)(24,28)(27,30)(29,31);(8,9)(10,13)(11,12)(14,15)(16,18,19,26)(17,21,23,25)(20,27,28,31)(22,29,24,30);(9,12)(13,15)(17,22)(20,28)(21,29)(23,24)(25,30)(27,31);(8,10,11,14)(9,13,12,15)(17,23)(21,25)(22,24)(29,30)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17331);