Finite Group DatabasebetaFinite Group Databasebeta| order | 23604 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C22×C281 ⋊ C3×C7 |
| Hall | C22×C281⋊C7 ⋊ C3 |
| Hall | A4×C281 ⋊ C7 |
| Sylow | C281 ⋊ C7×A4 |
| Sylow | C22 ⋊ C3×C281⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C281 | C3×C7 |
| LCS | G ▷ C22×C281 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1124 |
188 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23604, 21);