Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | Aut(G) order 88080384 |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C43 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, prime radical, cosocle | C24 | C24 |
| commutator | C23 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
1143 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 256 |
A minimal faithful permutation representation — 4 generators on 16 points:
(2,4)(6,7)(10,11)(13,14,15,16);(5,6,8,7);(9,10,12,11);(1,2,3,4)(5,7,8,6)(9,11,12,10)Polycyclic presentation:
2^8|a^2=h,b^2=e,c^2=f,d^2=g,b^a=be,c^a=cf,d^a=dg88 conjugacy classes — view the full character table.
| Fitting subgroup of | C4⋊(#384⋊C3), #14692⋊C7 |
| maximal subgroup of | #109188, #109192, #116034, … |
| maximal normal subgroup of | #109188, #109192, #116034, … |
| maximal quotient of | #154085, #154174, #154183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 7680);