Finite Group DatabasebetaFinite Group Databasebeta| order | 18124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#11716161 |
| Fitting, socle, Hall | C23×C197 ⋊ C4 |
| derived, Sylow | C197 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #11716161 |
| commutator, hypocenter | C197 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C197 | C4 |
| prime radical | C23×D197 | C2 |
| cosocle | D197 | C2×C23 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C23 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4531 |
1219 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18124, 6);