Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C599⋊#95 |
| Sylow | C599 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D599 |
| commutator | C2×C599 | C42 |
| Fitting | C22×C4×C599 | C2 |
| socle, prime radical, cosocle | C23×C599 | C22 |
| hypercenter | C22×C4 | D599 |
| hypocenter | C599 | #95 |
| LCS | G ▷ C2×C599 ▷ C599 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19168 |
Polycyclic presentation:
2^5,599|a^2=d,b^2=e,b^a=bc,f^b=f^5984804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50305624, #50305625, #50305627, … |
| maximal normal subgroup of | #50305624, #50305625, #50305627, … |
| maximal quotient of | #50305644, #50305645, #50305646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 53);