Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | D4×#41×C83 ⋊ C2 |
| Sylow | C83 ⋊ #62748 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C26 |
| Frattini | C22 | C25×D83 |
| Fitting | D4×#41×C83 | C2 |
| hypercenter | D4×#41 | D83 |
| hypocenter | C83 | #62748 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C2×C4 ◁ D4×#41 | |
7280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|d^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dg,e^a=eh,c^b=cg,d^b=dh,i^d=i^822126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 1077220);