Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C2×C7×#540 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1260 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(3,4)(5,9)(6,7)(8,10)(12,15)(13,17);(4,7)(8,9)(11,12,14,15)(13,16,17,18);(3,4)(5,8)(6,7)(9,10)(11,12)(13,16)(14,15)(17,18);(3,5,6,10)(4,8,7,9)(11,13,14,17)(12,16,15,18)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19170);