Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×ΓL(1,𝔽8)⋊D175 |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊D175 |
| unambiguous semidirect product | (C2×C25)⋊(ΓL(1,𝔽8)⋊D7) |
| Fitting | C2×C72×C25 ⋊ C2×C3 |
| derived, Hall | C72×C25 ⋊ C22×C3 |
| Hall | C2×C7⋊D175 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8)×C25 ⋊ C22 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×D25 |
| Sylow | C72 ⋊ C2×C3×D25 |
| Sylow | C25 ⋊ C2×ΓL(1,𝔽8)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)⋊D175 |
| commutator, cosocle, hypocenter | C72×C25 | C22×C3 |
| Frattini | C5 | C2×C5⋊(ΓL(1,𝔽8)⋊D7) |
| Fitting | C2×C72×C25 | C2×C3 |
| socle | C2×C5×C72 | C3×D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 ◁ C2 | |
150 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 252);