Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#16809850 |
| Fitting, Hall | C7×C841 ⋊ C4 |
| derived, Sylow | C841 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #16809850 |
| commutator, hypocenter | C841 | C4×C7 |
| Frattini | C29 | C7×#1181 |
| Fitting | C7×C841 | C4 |
| socle | C7×C29 | #1181 |
| prime radical | C7×D841 | C2 |
| cosocle | D841 | C2×C7 |
| LCS | G ▷ C841 | |
| UCS | C1 ◁ C7 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5887 |
1498 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 11);