Finite Group DatabasebetaFinite Group Databasebeta| order | 19088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C1193 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #18012025 |
| commutator, hypocenter | C1193 | C2×C8 |
| Frattini | C2 | C2×#18012025 |
| Fitting | C4×C1193 | C4 |
| socle | C2×C1193 | C2×C4 |
| prime radical | C2×D1193 | C4 |
| cosocle | Dic1193 | C22 |
| LCS | G ▷ C1193 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9544 |
Polycyclic presentation:
2^4,1193|a^2=c,c^2=d,e^a=e^186,e^b=e^1192,e^c=e^11921208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#18012025, #50303026, #50303034, … |
| maximal normal subgroup of | C8×#18012025, #50303026, #50303034, … |
| maximal quotient of | C4×#23750848, #50303029, #50303039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 48);