Finite Group DatabasebetaFinite Group Databasebeta| order | 19088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C1193 ⋊ C2 |
| Sylow | C1193 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D1193 |
| commutator, socle, cosocle | C2×C1193 | C23 |
| Fitting | Q8×C1193 | C2 |
| hypercenter | Q8 | D1193 |
| hypocenter | C1193 | #41 |
| LCS | G ▷ C2×C1193 ▷ C1193 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9544 |
Polycyclic presentation:
2^4,1193|c^2=d,b^a=bd,e^a=e^1192,e^b=e^1192,e^c=e^11922990 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50302993, #50302995, #50302999, … |
| maximal normal subgroup of | #50302993, #50302995, #50302999, … |
| maximal quotient of | #50302930, #50302934, Q8×Dic1193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 41);