Finite Group DatabasebetaFinite Group Databasebeta| order | 14864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C929 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#16836500 |
| commutator, socle | C2×C929 | C2×C4 |
| Fitting | C4×C929 | C4 |
| prime radical | C2×D929 | C4 |
| cosocle | Dic929 | C22 |
| hypercenter | C4 | #16836500 |
| hypocenter | C929 | M16 |
| LCS | G ▷ C2×C929 ▷ C929 | |
| UCS | C1 ◁ C2 ◁ C4 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7432 |
Polycyclic presentation:
2^4,929|a^2=c,c^2=d,b^a=bd,e^a=e^605,e^b=e^928,e^c=e^928938 conjugacy classes — view the full character table.
| maximal subgroup of | #44446438, #44446439, #44446444, … |
| maximal normal subgroup of | #44446438, #44446439, #44446444, … |
| maximal quotient of | #44446429, #44446431, C4⋊#21418259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14864, 50);