Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#3566 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(9,15)(10,20)(11,25)(12,28)(16,33)(17,23)(19,32)(21,31)(24,37)(26,34)(27,38)(29,39);(8,9)(10,21)(11,26)(12,18)(13,15)(14,19)(16,20)(17,27)(22,28)(23,25)(24,33)(29,35)(30,32)(31,37)(34,38)(36,39);(8,10,13,24)(9,16,15,31)(11,22,27,18)(12,23,28,34)(14,20,30,37)(17,29,26,39)(19,21,32,33)(25,36,38,35);(8,11)(9,17)(10,22)(12,21)(13,27)(14,25)(15,26)(16,29)(18,24)(19,34)(20,36)(23,32)(28,33)(30,38)(31,39)(35,37);(8,12,14,29)(9,18,19,35)(10,23,20,26)(11,21,25,16)(13,28,30,39)(15,22,32,36)(17,24,34,37)(27,33,38,31)266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19284);