Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C7⋊#1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C24 |
| direct product | C2×C7⋊#1020 |
| unambiguous semidirect product | (C2×C7)⋊#1020 |
| Fitting, socle | C25×C7 ⋊ D3 |
| derived | C7×C22⋊A4 ⋊ C22 |
| Sylow | C7 ⋊ C2×#1020 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊#1020 |
| commutator, cosocle, hypocenter | C7×C22⋊A4 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C25×C7 | D3 |
| LCS | G ▷ C7×C22⋊A4 | |
| UCS | C1 ◁ C2 | |
476 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214032, C2×#72222237, C2×D7×#1020, … |
| maximal normal subgroup of | C2×#72214032, C2×D7×#1020, #72276689, … |
| maximal quotient of | C2×C7⋊#5935, #72230363, #72259523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11703);