Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63011 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C22 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
3339 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 6 generators on 32 points:
(1,2,6,8)(3,11,15,25)(4,10,16,22)(5,9,18,21)(7,12,20,14)(13,24,27,32)(17,23,29,31)(19,26,30,28);(1,3,5,14)(2,7,9,11)(4,13,17,28)(6,15,18,12)(8,20,21,25)(10,19,23,24)(16,27,29,26)(22,30,31,32);(2,8)(3,12)(7,11)(9,21)(10,22)(13,26)(14,15)(19,24)(20,25)(23,31)(27,28)(30,32);(2,9)(7,11)(8,21)(10,23)(19,24)(20,25)(22,31)(30,32);(1,4,5,17)(2,10,9,23)(3,13,14,28)(6,16,18,29)(7,19,11,24)(8,22,21,31)(12,26,15,27)(20,30,25,32);(4,16)(10,22)(13,27)(17,29)(19,30)(23,31)(24,32)(26,28)Polycyclic presentation:
2^8|a^2=h,b^2=g,e^2=g,b^a=bg,c^a=ch,d^a=dg,c^b=cgh,f^e=fh76 conjugacy classes — view the full character table.
| Fitting subgroup of | #63026⋊C3, #72258118 |
| maximal subgroup of | #511854, C2×#63026, #10586352, … |
| maximal normal subgroup of | #511854, C2×#63026, #10586352, … |
| maximal quotient of | #7627217, #7627252, #7627272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 56014);