Finite Group DatabasebetaFinite Group Databasebeta| order | 22100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C5 |
| direct product | C17×#13049918 |
| derived, Hall | C52×C13 ⋊ C4×C17 |
| Hall | C52×C13×C17 ⋊ C4 |
| Hall | C52×C17 ⋊ Dic13 |
| Hall | C13×C17 ⋊ #1039 |
| Sylow | C52 ⋊ C17×Dic13 |
| Sylow | C13 ⋊ C17×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | C5⋊D65 |
| commutator, hypocenter | C52×C13 | C4×C17 |
| Frattini | C2 | C17×C5⋊D65 |
| Fitting, socle, prime radical | C2×C52×C13×C17 | C2 |
| cosocle | C2×C52×C13 | C2×C17 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C2×C17 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22100 |
5576 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22100, 54);