Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C7⋊#1042 |
| Fitting, socle, derived, Hall | C52×C72 ⋊ C3×C4 |
| Hall | C7×C7⋊#1042 ⋊ C3 |
| Hall | C52×C7×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C7×ΓL(1,𝔽8) ⋊ #1042 |
| Sylow | C72 ⋊ C3×#1042 |
| Sylow | C52 ⋊ ΓL(1,𝔽8)×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C72 | C3×C4 |
| prime radical | C5×C7×D5×ΓL(1,𝔽8) | C2 |
| cosocle | C5×C72×D5 | C2×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
365 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 465);