Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D47 |
| commutator, socle | C2×C47 | C22×C4 |
| Fitting, prime radical | #41×C47 | C2 |
| cosocle | C4×C47 | C23 |
| hypercenter | #41 | D47 |
| hypocenter | C47 | #131 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 752 |
Polycyclic presentation:
2^5,47|a^2=d,d^2=e,f^a=f^46,c^b=ce250 conjugacy classes — view the full character table.
| maximal subgroup of | #15689237, #15689240, #15689242, … |
| maximal normal subgroup of | #15689237, #15689240, #15689242, … |
| maximal quotient of | #15689079, #15689090, #15689150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 153);