Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #37644 |
| automorphism | Aut(G) order 65536 |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
1555 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 5 generators on 24 points:
(6,8)(9,10,14,13)(11,17,19,15)(12,20,21,16)(18,22,24,23);(2,4)(9,11,14,19)(10,15,13,17)(12,18,21,24)(16,22,20,23);(1,2)(3,4)(5,6)(7,8)(9,11)(10,15)(12,18)(13,17)(14,19)(16,22)(20,23)(21,24);(9,12,14,21)(10,16,13,20)(11,18,19,24)(15,22,17,23);(1,2)(3,4)(9,13,14,10)(11,17,19,15)(12,20,21,16)(18,23,24,22)Polycyclic presentation:
2^8|a^2=f,b^2=f,d^2=f,e^2=f,b^a=bf,c^a=cg,d^a=df,c^b=ch,e^b=efh58 conjugacy classes — view the full character table.
| maximal subgroup of | #6533396, #6533400, #6533404, … |
| maximal normal subgroup of | #6533396, #6533400, #6533404, … |
| maximal quotient of | #521320, #522069, #522580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 30647);