Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C211 · Schur multiplier (H2) = C254 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C4 | C210 |
| commutator, Frattini, cosocle | C2 | C211 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ G | |
| LECS | G ▷ C2 ▷ C1 | |
8935217648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
Polycyclic presentation:
2^12|a^2=l,b^2=l,k^2=l,b^a=bl,d^c=dl,f^e=fl,h^g=hl,j^i=jl2050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | 2−1+12, H(13,𝔽2), C2×#72274291 |
| maximal normal subgroup of | 2−1+12, H(13,𝔽2), C2×#72274291 |
| maximal quotient of | C2×#72274291 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.12);;
gap> SetPower(coll, 2, F.12);;
gap> SetPower(coll, 11, F.12);;
gap> SetConjugate(coll, 2, 1, F.2*F.12);;
gap> SetConjugate(coll, 4, 3, F.4*F.12);;
gap> SetConjugate(coll, 6, 5, F.6*F.12);;
gap> SetConjugate(coll, 8, 7, F.8*F.12);;
gap> SetConjugate(coll, 10, 9, F.10*F.12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);