Finite Group DatabasebetaFinite Group Databasebeta| order | 22100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×#11725133 |
| Fitting, socle, Hall | C52×C13×C17 ⋊ C4 |
| derived, Hall | C13×C17 ⋊ C4×C52 |
| Hall | C52×C17 ⋊ Dic13 |
| Hall | C52×C13 ⋊ #595 |
| Sylow | C17 ⋊ C52×Dic13 |
| Sylow | C13 ⋊ C52×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | #11725133 |
| commutator, hypocenter | C13×C17 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C17 | C4 |
| prime radical | C52×C13×D17 | C2 |
| cosocle | C13×D17 | C2×C52 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 ◁ C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5525 |
1700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22100, 70);