Finite Group DatabasebetaFinite Group Databasebeta| order | 14944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D8×C467 ⋊ C2 |
| Sylow | C467 ⋊ AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D467 |
| commutator, cosocle | C4×C467 | C23 |
| Frattini | C4 | C22×D467 |
| Fitting | D8×C467 | C2 |
| socle | C2×C467 | C2×D4 |
| hypercenter | D8 | D467 |
| hypocenter | C467 | AGL(1,ℤ/8) |
| LCS | G ▷ C4×C467 ▷ C2×C467 ▷ C467 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3736 |
Polycyclic presentation:
2^5,467|d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^c=f^4661642 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/8)×D467, C2×#28417977, #44470833, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D467, C2×#28417977, #44470833, … |
| maximal quotient of | #44470035, #44470040, #44470078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14944, 170);