Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×#14556582 |
| Sylow | C73 ⋊ C4×#125 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D73 |
| commutator | C22×C73 | C23×C4 |
| Frattini | C23 | C23×D73 |
| Fitting | C4×C4⋊C4×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C4×C4⋊C4 | D73 |
| hypocenter | C73 | C4×#125 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
484 conjugacy classes of subgroups.
1496 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32985971, #32985973, #32985976, … |
| maximal normal subgroup of | #32985971, #32985973, #32985976, … |
| maximal quotient of | C4×#17988474, C4×#17988470, C4×#17988486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 7068);