Finite Group DatabasebetaFinite Group Databasebeta| order | 19288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D2411 |
| Fitting | C4×C2411 ⋊ C2 |
| derived, Sylow | C2411 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D2411 |
| commutator, hypocenter | C2411 | C2×C4 |
| Frattini | C2 | C2×D2411 |
| Fitting | C4×C2411 | C2 |
| socle, cosocle | C2×C2411 | C22 |
| prime radical | C2×D2411 | C2 |
| LCS | G ▷ C2411 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9644 |
4828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D2411, #50310800, C2×C4×D2411, … |
| maximal normal subgroup of | C8×D2411, #50310800, C2×C4×D2411, … |
| maximal quotient of | C4×Dic2411, (C2×D2411)⋊C4, Dic2411⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19288, 7);