Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C5⋊(C5⋊#64418) |
| unambiguous semidirect product | (C2×C5)⋊(C5⋊#64418) |
| Fitting, socle | C2×C52×C72 ⋊ D3 |
| derived, Hall | C52×#3862 ⋊ C22 |
| Hall | C52×C72 ⋊ C2×D3 |
| Hall | #3862 ⋊ C2×C5⋊D5 |
| Sylow | C72 ⋊ C2×C3⋊(C5⋊D5) |
| Sylow | C52 ⋊ C2×#64418 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(C5⋊#64418) |
| commutator, cosocle, hypocenter | C52×#3862 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C72 | D3 |
| LCS | G ▷ C52×#3862 | |
| UCS | C1 ◁ C2 | |
272 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 608);