Finite Group DatabasebetaFinite Group Databasebeta| order | 14752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C461 ⋊ C2 |
| Sylow | C461 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D461 |
| commutator, socle, cosocle | C22×C461 | C23 |
| Fitting | C4⋊C4×C461 | C2 |
| prime radical | C22×D461 | C22 |
| hypercenter | C4⋊C4 | D461 |
| hypocenter | C461 | #126 |
| LCS | G ▷ C22×C461 ▷ C461 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7376 |
Polycyclic presentation:
2^5,461|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^460,f^c=f^4602314 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D461, C2×#28414113, #44442603, … |
| maximal normal subgroup of | #126×D461, C2×#28414113, #44442603, … |
| maximal quotient of | #44441943, #44441957, #44441959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14752, 141);