Finite Group DatabasebetaFinite Group Databasebeta| order | 14752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C461 ⋊ C2 |
| Sylow | C461 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D461 |
| commutator, socle | C2×C461 | C22×C4 |
| Fitting | M16×C461 | C2 |
| prime radical | #20301501 | C2 |
| cosocle | C4×C461 | C23 |
| hypercenter | M16 | D461 |
| hypocenter | C461 | #131 |
| LCS | G ▷ C2×C461 ▷ C461 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7376 |
Polycyclic presentation:
2^5,461|a^2=d,d^2=e,f^a=f^460,c^b=ce,f^c=f^4602320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44442190, #44442192, #44442195, … |
| maximal normal subgroup of | #44442190, #44442192, #44442195, … |
| maximal quotient of | #44442033, #44442034, #44442041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14752, 154);