Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×#14556497 |
| derived, Sylow | C73 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D73 |
| commutator, hypocenter | C73 | C22×C32 |
| Frattini | C16 | C22×D73 |
| Fitting | C22×C16×C73 | C2 |
| socle | C23×C73 | C16 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
2432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32973670, #32973671, #32973682, … |
| maximal normal subgroup of | #32973670, #32973671, #32973682, … |
| maximal quotient of | C2×C4×#14556497, C2×C22⋊#14556497, C2×C4⋊#14556497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6799);