Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#3586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | C23×D4 |
| commutator, Frattini, cosocle | C4 | C25×C7 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C7×#41 ◁ G | |
1412 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)(8,9)(10,18)(11,15)(12,24)(13,16)(14,20)(17,26)(19,32)(21,31)(22,29)(23,36)(25,28)(27,34)(30,35)(33,39)(37,38);(8,10,13,21)(9,14,16,28)(11,19,22,33)(12,25,26,20)(15,27,29,38)(17,31,24,18)(23,37,35,34)(30,39,36,32);(8,11)(9,15)(10,19)(12,23)(13,22)(14,27)(16,29)(17,30)(18,32)(20,34)(21,33)(24,36)(25,37)(26,35)(28,38)(31,39);(11,22)(15,29)(19,33)(23,35)(27,38)(30,36)(32,39)(34,37);(9,16)(14,28)(15,29)(17,24)(18,31)(27,38)(30,36)(32,39)287 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19304);