Finite Group DatabasebetaFinite Group Databasebeta| order | 21088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C659 ⋊ C2 |
| Sylow | C659 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D659 |
| commutator, cosocle | C4×C659 | C23 |
| Frattini | C4 | C22×D659 |
| Fitting | SD16×C659 | C2 |
| socle | C2×C659 | C2×D4 |
| hypercenter | SD16 | D659 |
| hypocenter | C659 | #135 |
| LCS | G ▷ C4×C659 ▷ C2×C659 ▷ C659 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10544 |
Polycyclic presentation:
2^5,659|c^2=e,d^2=e,b^a=bd,d^a=de,d^b=de,f^b=f^658,f^c=f^6582317 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21088, 167);