Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#17989388 |
| Fitting | C22×D8×C73 ⋊ C2 |
| Sylow | C73 ⋊ C2×#576 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D73 |
| commutator | C4×C73 | C25 |
| Frattini | C4 | C24×D73 |
| Fitting | C22×D8×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | C22×D8 | D73 |
| hypocenter | C73 | C2×#576 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×D8 | |
1512 conjugacy classes of subgroups.
1052 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33001668, #33001680, #33001707, … |
| maximal normal subgroup of | #33001668, #33001680, #33001707, … |
| maximal quotient of | C2×#22618452, C2×#22618527, C2×#22618756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19259);