Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #2263 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#2263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C23×C7 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C2×C7×C8 ◁ C2×C7×C16 ◁ G | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,23)(12,26)(13,15)(16,19)(17,20)(18,24)(21,33)(22,27)(25,39)(28,35)(29,34)(30,36)(31,37)(32,38);(9,14)(10,19)(11,20)(12,24)(15,27)(16,17)(18,33)(21,38)(22,36)(23,28)(25,37)(26,29)(30,31)(32,39)(34,35);(9,15)(14,27)(16,30)(17,31)(18,26)(23,39)(28,32)(29,33)182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5498);