Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C73 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#10596842 |
| commutator, socle | C2×C73 | C2×C16 |
| Fitting | C8×C73 | C8 |
| prime radical | C2×D73 | C16 |
| cosocle | #11924031 | C22 |
| hypercenter | C8 | #10596842 |
| hypocenter | C73 | M64 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C8 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^6,73|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^10,g^b=g^72,g^c=g^27,g^d=g^72112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 1658);