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 | C7×2−1+6 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | C26 |
| commutator, Frattini, cosocle | C2 | C26×C7 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ G | |
5796 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 6 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,15)(11,16)(12,24)(13,14)(17,25)(18,28)(19,33)(20,26)(21,30)(22,36)(23,27)(29,34)(31,37)(32,39)(35,38);(9,14)(15,26)(16,27)(17,24)(28,30)(29,33)(31,36)(38,39);(8,10,13,20)(9,15,14,26)(11,21,23,18)(12,19,25,34)(16,30,27,28)(17,29,24,33)(22,35,37,32)(31,39,36,38);(8,11,13,23)(9,16,14,27)(10,18,20,21)(12,22,25,37)(15,28,26,30)(17,31,24,36)(19,32,34,35)(29,38,33,39);(8,9)(10,15)(11,16)(12,17)(13,14)(18,28)(19,29)(20,26)(21,30)(22,31)(23,27)(24,25)(32,38)(33,34)(35,39)(36,37);(8,12)(9,17)(10,19)(11,22)(13,25)(14,24)(15,29)(16,31)(18,32)(20,34)(21,35)(23,37)(26,33)(27,36)(28,38)(30,39)455 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19343);