Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C83×Q128 ⋊ C2 |
| Sylow | C83 ⋊ #13741 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D32×D83 |
| commutator, cosocle | C32×C83 | C23 |
| Frattini | C32 | C22×D83 |
| Fitting | C83×Q128 | C2 |
| socle | C2×C83 | C2×D32 |
| hypercenter | Q128 | D83 |
| hypocenter | C83 | #13741 |
| LCS | G ▷ C32×C83 ▷ C16×C83 ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ Q128 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10624 |
Polycyclic presentation:
2^8,83|c^2=h,d^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=de,e^a=ef,f^a=fg,g^a=gh,i^a=i^82,d^b=de,e^b=ef,f^b=fg,g^b=gh,i^b=i^82,i^c=i^821505 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 90623);