Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C83×#2847 ⋊ C2 |
| Sylow | C83 ⋊ #36607 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D83 |
| commutator, socle, cosocle | C23×C83 | C25 |
| Fitting | C83×#2847 | C2 |
| hypercenter | #2847 | D83 |
| hypocenter | C83 | #36607 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #2847 | |
2524 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=h,b^2=gh,c^2=fh,d^2=gh,e^2=fh,b^a=bf,c^a=cg,i^a=i^82,c^b=ch,e^b=eh,d^c=dh,i^c=i^82,e^d=eh,i^e=i^821874 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 375372);