Finite Group DatabasebetaFinite Group Databasebeta| order | 14864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C929 ⋊ C2 |
| Sylow | C929 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D929 |
| commutator, socle, cosocle | C2×C929 | C23 |
| Fitting | Q8×C929 | C2 |
| hypercenter | Q8 | D929 |
| hypocenter | C929 | #41 |
| LCS | G ▷ C2×C929 ▷ C929 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7432 |
Polycyclic presentation:
2^4,929|c^2=d,b^a=bd,e^a=e^928,e^b=e^928,e^c=e^9282330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44446395, #44446397, #44446401, … |
| maximal normal subgroup of | #44446395, #44446397, #44446401, … |
| maximal quotient of | #44446332, #44446336, Q8×Dic929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14864, 41);