Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×C22⋊#64408 |
| Fitting | C22×D4×C73 ⋊ C4 |
| Sylow | C73 ⋊ D4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | C22×D4×C73 | C4 |
| hypercenter | C22×D4 | #64408 |
| hypocenter | C73 | D4×C22⋊C4 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
1252 conjugacy classes of subgroups.
410 conjugacy classes — view the full character table.
| maximal subgroup of | #34006648, #34006649, #34006656, … |
| maximal normal subgroup of | #34006648, #34006649, #34006656, … |
| maximal quotient of | C22⋊C4×C22⋊#64408, C4⋊C4×C22⋊#64408, D4×(C2×#64408)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21012);