Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C73 ⋊ C2 |
| Sylow | C73 ⋊ #508 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D8×D73 |
| commutator, cosocle | C8×C73 | C23 |
| Frattini | C8 | C22×D73 |
| Fitting | D16×C73 | C2 |
| socle | C2×C73 | C2×D8 |
| hypercenter | D16 | D73 |
| hypocenter | C73 | #508 |
| LCS | G ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D16 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^6,73|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,d^b=de,e^b=ef,g^c=g^72418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 978);