Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#2830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C7 |
| prime radical | C22×C7×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
408 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)(13,15)(16,17,20,21)(18,22,23,19)(24,25,28,31)(26,27,30,29);(10,14)(13,15)(18,23)(19,22)(24,26,28,30)(25,29,31,27);(8,9)(10,13)(11,12)(14,15)(16,18)(17,19)(20,23)(21,22)(24,26)(25,29)(27,31)(28,30);(8,10)(9,13)(11,14)(12,15)(16,19)(17,18)(20,22)(21,23)(24,27,28,29)(25,30,31,26)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16905);