Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D47 |
| commutator, socle, cosocle | C22×C47 | C23 |
| Fitting, prime radical | C2×D4×C47 | C2 |
| hypercenter | C2×D4 | D47 |
| hypocenter | C47 | #124 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 752 |
Polycyclic presentation:
2^5,47|b^2=e,c^2=d,b^a=bd,c^a=ce,f^b=f^46,f^c=f^46244 conjugacy classes — view the full character table.
| maximal subgroup of | #15688917, #15689294, #15689301, … |
| maximal normal subgroup of | #15688917, #15689294, #15689301, … |
| maximal quotient of | #15688988, #15689017, #15689026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 133);