Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#3497 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
1492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 27 points:
(1,2,3,4,5,6,7)(9,11)(13,14)(16,24)(18,20)(22,27);(12,13,17,14)(15,20,23,18)(16,19,24,21)(22,26,27,25);(8,9,10,11)(12,14,17,13)(15,20,23,18)(16,21,24,19)(22,26,27,25);(12,15,17,23)(13,18,14,20)(16,22,24,27)(19,25,21,26);(12,16)(13,19)(14,21)(15,22)(17,24)(18,25)(20,26)(23,27)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19215);