Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×#14556686 |
| derived, Sylow | C73 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #10596842 |
| commutator, hypocenter | C73 | C22×C16 |
| Frattini | C2 | C22×#10596842 |
| Fitting | C2×C4×C73 | C8 |
| socle | C22×C73 | C2×C8 |
| prime radical | C22×D73 | C8 |
| cosocle | #10596833 | C23 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C4 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 1666);