Finite Group DatabasebetaFinite Group Databasebeta| order | 14816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×C463⋊C8 |
| derived, Sylow | C463 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D463 |
| commutator, hypocenter | C463 | C22×C8 |
| Frattini | C4 | C22×D463 |
| Fitting | C22×C4×C463 | C2 |
| socle, prime radical | C23×C463 | C4 |
| cosocle | C4×C463 | C23 |
| LCS | G ▷ C463 | |
| UCS | C1 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14816 |
3728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44444547, #44444548, #44444555, … |
| maximal normal subgroup of | #44444547, #44444548, #44444555, … |
| maximal quotient of | C2×C4×C463⋊C8, C2×C22⋊(C463⋊C8), C2×C4⋊(C463⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14816, 148);