Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C214 |
| direct product | C7×H(7,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | C26 |
| commutator, Frattini, cosocle | C2 | C26×C7 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ G | |
5992 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 6 generators on 23 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,18)(12,13)(15,19)(16,20)(17,23)(21,22);(9,13)(14,20)(15,18)(21,23);(10,16)(14,20)(17,22)(21,23);(8,10)(9,14)(11,17)(12,16)(13,20)(15,21)(18,23)(19,22);(8,9)(10,14)(11,15)(12,13)(16,20)(17,21)(18,19)(22,23);(8,11)(9,15)(10,17)(12,19)(13,18)(14,21)(16,22)(20,23)455 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19342);