Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#2026 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
258 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7)(12,13,15,17)(14,18,19,16)(20,21,23,25)(22,28,29,35)(24,32,31,27)(26,33,34,30);(8,9)(10,11)(12,14,15,19)(13,16,17,18)(21,25)(26,34)(27,32)(28,35);(9,11)(20,22,23,29)(21,26,25,34)(24,33,31,30)(27,35,32,28)224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5261);