Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1284 |
| automorphism | Aut(G) order 16384 |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#1285 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #95 |
| commutator | C2×C4 | C2×C42 |
| Frattini, cosocle | C2×C42 | C23 |
| prime radical | C24 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
373 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2);(3,4,6,9,7,10,5,8)(11,12,13,16,14,15,17,18);(4,8,10,9)(12,15)(13,17)64 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#1285, #105393, #105532, … |
| maximal normal subgroup of | C4×#1285, #105393, #105532, … |
| maximal quotient of | C2×#7017, #94959, #94969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 935);