Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | Aut(G) order 704643072 |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C43 |
| direct product | C2×#2867 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C24 |
| commutator, Frattini, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
4047 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 5 generators on 14 points:
(1,2);(4,6)(8,9)(12,13);(7,8,10,9);(11,12,14,13);(3,4,5,6)(7,9,10,8)(11,13,14,12)88 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 29630);