Finite Group DatabasebetaFinite Group Databasebeta| order | 256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
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 | |
5493 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 6 generators on 36 points:
(2,4)(6,12)(7,13)(10,24)(14,21)(16,26)(19,32)(22,34)(31,36);(1,2)(3,4)(5,6,11,12)(7,8,13,20)(9,21,23,14)(10,15,24,25)(16,29,26,18)(17,19,27,32)(22,33,34,28)(30,36,35,31);(5,7)(6,8)(9,16)(10,17)(11,13)(12,20)(14,18)(15,19)(21,29)(22,30)(23,26)(24,27)(25,32)(28,31)(33,36)(34,35);(5,8)(6,13)(7,12)(9,18)(10,19)(11,20)(14,26)(15,27)(16,21)(17,25)(22,31)(23,29)(24,32)(28,35)(30,33)(34,36);(5,9,11,23)(6,14,12,21)(7,16,13,26)(8,18,20,29)(10,22,24,34)(15,28,25,33)(17,30,27,35)(19,31,32,36);(5,10)(6,15)(7,17)(8,19)(9,22)(11,24)(12,25)(13,27)(14,28)(16,30)(18,31)(20,32)(21,33)(23,34)(26,35)(29,36)Polycyclic presentation:
2^8|b^2=h,e^2=h,b^a=bg,c^a=ch,f^a=fh,e^b=eh,d^c=dh82 conjugacy classes — view the full character table.
| Fitting subgroup of | #62859⋊C3 |
| maximal subgroup of | #359530, #359535, #359653, … |
| maximal normal subgroup of | #359530, #359535, #359653, … |
| maximal quotient of | #7625697, #7625700, #7625701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 55847);