Finite Group DatabasebetaFinite Group Databasebeta| order | 22388 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#11715871 |
| Fitting, socle, Hall | C29×C193 ⋊ C4 |
| derived, Sylow | C193 ⋊ C4×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #11715871 |
| commutator, hypocenter | C193 | C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C193 | C4 |
| prime radical | C29×D193 | C2 |
| cosocle | D193 | C2×C29 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C29 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5597 |
1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22388, 6);