Finite Group DatabasebetaFinite Group Databasebeta| order | 14752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#20301504 |
| derived, Sylow | C461 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14270406 |
| commutator, hypocenter | C461 | C2×C16 |
| Frattini | C4 | C2×#14270406 |
| Fitting | C2×C4×C461 | C4 |
| socle, prime radical | C22×C461 | C8 |
| cosocle | #16814779 | C22 |
| LCS | G ▷ C461 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14752 |
952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#20301504, #44442962, #44442964, … |
| maximal normal subgroup of | C4×#20301504, #44442962, #44442964, … |
| maximal quotient of | C4×#20301504, C22⋊#20301504, C4⋊#20301504, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14752, 218);