Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#64408 |
| commutator, socle | C2×C73 | C22×C8 |
| Fitting | M16×C73 | C4 |
| prime radical | #11924028 | C4 |
| cosocle | #10596831 | C23 |
| hypercenter | M16 | #64408 |
| hypocenter | C73 | #504 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ M16 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^6,73|a^2=d,d^2=e,e^2=f,g^a=g^27,c^b=cf,g^b=g^72,g^d=g^72220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 1608);