Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C83×#2678 ⋊ C2 |
| Sylow | C83 ⋊ #36724 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D83 |
| commutator, socle, cosocle | C23×C83 | C25 |
| Fitting | C83×#2678 | C2 |
| hypercenter | #2678 | D83 |
| hypocenter | C83 | #36724 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #2678 | |
2644 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=fg,e^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,c^b=ch,d^b=dfh,i^c=i^82,i^d=i^82,i^e=i^821364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 376638);