Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #47826 |
| automorphism | Aut(G) order 65536 |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
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 | |
1438 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 5 generators on 20 points:
(2,4)(5,6,9,10)(7,8,11,12)(13,14,18,20)(15,19,16,17);(6,10)(7,11)(13,15)(14,19)(16,18)(17,20);(1,2)(3,4)(14,20)(15,16);(5,7)(6,8)(9,11)(10,12)(13,16,18,15)(14,17,20,19);(5,8)(6,7)(9,12)(10,11)(13,17)(14,15)(16,20)(18,19)Polycyclic presentation:
2^8|a^2=fh,d^2=h,b^a=bf,c^a=cg,e^a=ef,c^b=ch,d^b=dfh,e^b=eh,d^c=dh52 conjugacy classes — view the full character table.
| maximal subgroup of | #133407, #499807, #500226, … |
| maximal normal subgroup of | #133407, #499807, #500226, … |
| maximal quotient of | #560404, #561492, #562663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 43844);