Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#14556679 |
| Sylow | C73 ⋊ C4×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#64408 |
| commutator | C2×C73 | C22×C42 |
| Frattini | C22 | C23×#64408 |
| Fitting | C4×Q8×C73 | C4 |
| socle | C22×C73 | C23×C4 |
| hypercenter | C4×Q8 | #64408 |
| hypocenter | C73 | C4×#131 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
572 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
440 conjugacy classes — view the full character table.
| maximal subgroup of | #34003565, #34003569, #34003574, … |
| maximal normal subgroup of | #34003565, #34003569, #34003574, … |
| maximal quotient of | C8×#14556679, #34015687, #34015754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21079);