Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×C19⋊C8 |
| derived, Sylow | C19 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D19 |
| commutator, hypocenter | C19 | C42×C8 |
| Frattini | C22×C4 | C22×D19 |
| Fitting | C43×C19 | C2 |
| socle, prime radical | C23×C19 | C22×C4 |
| cosocle | C22×C4×C19 | C23 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C43 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2432 |
704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #18069066, C4×C8×C19⋊C8, C4×#11926265, … |
| maximal normal subgroup of | #18069066, C4×C8×C19⋊C8, C4×#11926265, … |
| maximal quotient of | C4×C8×C19⋊C8, C4×#11926265, #97×C19⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 4192);