Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #15257 |
| automorphism | Aut(G) order 65536 |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C24 | C24 |
| prime radical | C25 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
707 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 4 generators on 24 points:
(2,4)(6,8)(9,10,13,12)(11,15,16,14)(18,21)(19,23);(10,12)(14,15)(17,18,20,21)(19,24,23,22);(5,6,7,8)(9,11)(10,14)(12,15)(13,16)(17,18)(19,22)(20,21)(23,24);(1,2)(3,4)(9,12,13,10)(11,15,16,14)(17,19,20,23)(18,22,21,24)Polycyclic presentation:
2^8|a^2=eg,b^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=dh,c^b=cg,d^b=de58 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#15677, #609316, #609393, … |
| maximal normal subgroup of | C2×#15677, #609316, #609393, … |
| maximal quotient of | #154735, #154757, #154856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 8665);