Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×C8×#64408 |
| Fitting | C4×C8×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #64408 |
| commutator, hypocenter | C73 | C42×C8 |
| Frattini | C2×C4 | C22×#64408 |
| Fitting | C4×C8×C73 | C4 |
| socle | C22×C73 | C2×C42 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C4×C8 | |
408 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
704 conjugacy classes — view the full character table.
| maximal subgroup of | #34000181, C82×#64408, #322×#64408, … |
| maximal normal subgroup of | #34000181, C82×#64408, #322×#64408, … |
| maximal quotient of | C82×#64408, C4×C8×#10596833, #322×#64408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20161);