Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D47 |
| commutator, socle, cosocle | C22×C47 | C23 |
| Fitting | C22×C4×C47 | C2 |
| prime radical | C2×C22⋊D47 | C2 |
| hypercenter | C22×C4 | D47 |
| hypocenter | C47 | #123 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 752 |
Polycyclic presentation:
2^5,47|c^2=d,b^a=bd,c^a=ce,f^a=f^46382 conjugacy classes — view the full character table.
| maximal subgroup of | #15689312, #123×D47, C2×#13094007, … |
| maximal normal subgroup of | #15689312, #123×D47, C2×#13094007, … |
| maximal quotient of | #15688986, #15688996, #15689002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 129);