Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#19150306 |
| Fitting, socle | C3×C72×C19 ⋊ C2×C3 |
| derived, Hall | C72×C19 ⋊ C2×C32 |
| Hall | C3×C7×#87704 ⋊ C2 |
| Hall | C7⋊D133 ⋊ C32 |
| Sylow | C72 ⋊ C3×D19⋊C3 |
| Sylow | C19 ⋊ C3×ΓL(1,𝔽8)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19150306 |
| commutator, cosocle, hypocenter | C72×C19 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1197 |
507 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#11716321⋊D7, C3×D7×#11716327, C3×#11716325⋊D7, … |
| maximal normal subgroup of | C3×#11716321⋊D7, C3×D7×#11716327, C3×#11716325⋊D7, … |
| maximal quotient of | C3×#26013839, C2×C3×#19150306 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 310);