Finite Group DatabasebetaFinite Group Databasebeta| order | 14816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C463 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D463 |
| commutator, socle, prime radical, cosocle | C22×C463 | C23 |
| Fitting | C2×Q8×C463 | C2 |
| hypercenter | C2×Q8 | D463 |
| hypocenter | C463 | C4⋊Q8 |
| LCS | G ▷ C22×C463 ▷ C463 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14816 |
Polycyclic presentation:
2^5,463|a^2=d,b^2=d,c^2=e,b^a=bd,c^a=ce,f^c=f^4622324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44444591, #44444974, #44444976, … |
| maximal normal subgroup of | #44444591, #44444974, #44444976, … |
| maximal quotient of | #44444662, #44444688, #44444698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14816, 144);