Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C5 |
| direct product | C17×#11744634 |
| derived, Hall | C52⋊C9 ⋊ C4×C17 |
| Hall | C17×C52⋊C9 ⋊ C4 |
| Hall | C52×C17 ⋊ Dic9 |
| Sylow | C52 ⋊ C17×Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #11744634 |
| commutator, hypocenter | C52⋊C9 | C4×C17 |
| Frattini | C3 | C17×#64480 |
| Fitting, socle | C3×C52×C17 | Dic3 |
| prime radical | C3×C17×C5⋊D5 | D3 |
| cosocle | (C5⋊D5)⋊C9 | C2×C17 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C17 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 765 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 141);