Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C2×C42 |
| direct product | C7×#2736 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C7 |
| prime radical | C25×C7 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,12)(13,15)(16,17,20,21)(18,22,23,19)(24,25,27,29)(26,30,31,28);(9,12)(10,15)(17,21)(19,22)(24,25,27,29)(26,28,31,30);(8,10)(9,13)(11,15)(12,14)(16,18)(17,19)(20,23)(21,22)(24,25)(26,28)(27,29)(30,31);(8,9)(10,13)(11,12)(14,15)(16,19)(17,18)(20,22)(21,23)(24,26)(25,28)(27,31)(29,30)224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16811);