Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×#532×C83 ⋊ C2 |
| Sylow | C83 ⋊ #34738 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C25 |
| Frattini | C23 | C24×D83 |
| Fitting | C2×#532×C83 | C2 |
| hypercenter | C2×#532 | D83 |
| hypocenter | C83 | #34738 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#532 | |
5570 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|b^2=f,e^2=g,b^a=bf,c^a=cg,c^b=ch,d^b=dh,i^c=i^82,i^d=i^822372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 338341);