Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C53 · Schur multiplier (H2) = C2 |
| direct product | D8×C53 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | D4 |
| commutator, Frattini, cosocle | C4 | C22×C53 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C4×C53 ◁ G | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 424 |
A minimal faithful permutation representation — 2 generators on 61 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61);(2,8)(3,7)(4,6)371 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 25);