Finite Group DatabasebetaFinite Group Databasebeta| order | 23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4×D373 |
| Fitting | C23×C4×C373 ⋊ C2 |
| derived, Sylow | C373 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D373 |
| commutator, hypocenter | C373 | C24×C4 |
| Frattini | C2 | C24×D373 |
| Fitting | C23×C4×C373 | C2 |
| socle | C24×C373 | C22 |
| prime radical | C24×D373 | C2 |
| cosocle | C2×C373 | C25 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11936 |
6016 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23872, 1367);