Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #45438 |
| 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 | |
1053 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 5 generators on 28 points:
(2,4)(7,11)(10,12)(13,14,17,20)(15,21,23,18)(16,24,26,19)(22,27,25,28);(6,9)(7,11)(13,15,17,23)(14,18,20,21)(16,25,26,22)(19,28,24,27);(1,2)(3,4)(5,6)(7,10)(8,9)(11,12)(13,15)(14,18)(16,22)(17,23)(19,27)(20,21)(24,28)(25,26);(5,7,8,11)(6,10,9,12)(13,14)(15,18)(16,19)(17,20)(21,23)(22,27)(24,26)(25,28);(5,6)(7,10)(8,9)(11,12)(13,16,17,26)(14,19,20,24)(15,22,23,25)(18,27,21,28)Polycyclic presentation:
2^8|a^2=f,b^2=f,d^2=fh,e^2=f,b^a=bf,c^a=cg,d^a=dh,e^a=ef,c^b=ch,d^b=dfh,e^b=eh52 conjugacy classes — view the full character table.
| maximal subgroup of | #98466, #246779, #246780, … |
| maximal normal subgroup of | #98466, #246779, #246780, … |
| maximal quotient of | #557039, #557052, #557362, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 38963);