Finite Group DatabasebetaFinite Group Databasebeta| order | 14816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C463 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D463 |
| commutator | C2×C463 | C22×C4 |
| Fitting | C4⋊C4×C463 | C2 |
| socle, prime radical, cosocle | C22×C463 | C23 |
| hypercenter | C4⋊C4 | D463 |
| hypocenter | C463 | C4×Q8 |
| LCS | G ▷ C2×C463 ▷ C463 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14816 |
Polycyclic presentation:
2^5,463|a^2=e,b^2=d,c^2=de,b^a=bd,f^c=f^4622330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44444880, #44444884, #44444885, … |
| maximal normal subgroup of | #44444880, #44444884, #44444885, … |
| maximal quotient of | #44444644, C4⋊C4×Dic463, #44444674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14816, 111);