Finite Group DatabasebetaFinite Group Databasebeta| order | 17700 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C59 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C59×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C2×C5⋊D5)⋊(C3×C59) |
| unambiguous semidirect product | (C2×C5⋊D5×C59)⋊C3 |
| Fitting, socle | C2×C52×C59 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C22×C3×C59 |
| Hall | C2×C5⋊D5×C59 ⋊ C3 |
| Hall | C59×C52⋊C3 ⋊ C22 |
| Hall | C52×C59 ⋊ C22×C3 |
| Hall | C2×C5⋊D5 ⋊ C3×C59 |
| Hall | C52⋊C3 ⋊ C22×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C59 | (C5⋊D5)⋊C3 |
| commutator, cosocle, hypocenter | C52 | C22×C3×C59 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C59 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C59 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1770 |
1180 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17700, 59);