Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C599 ⋊ C2 |
| Sylow | C599 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D599 |
| commutator, socle, cosocle | C22×C599 | C23 |
| Fitting | C2×Q8×C599 | C2 |
| prime radical | C2×D2396 | C2 |
| hypercenter | C2×Q8 | D599 |
| hypocenter | C599 | #124 |
| LCS | G ▷ C22×C599 ▷ C599 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9584 |
Polycyclic presentation:
2^5,599|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^598,f^b=f^598,f^c=f^5983004 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50305686, #50306063, #50306065, … |
| maximal normal subgroup of | #50305686, #50306063, #50306065, … |
| maximal quotient of | #50305755, #50305780, #50305791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 135);