Finite Group DatabasebetaFinite Group Databasebeta| order | 9376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#17989811 |
| Sylow | C293 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#11924078 |
| commutator | C2×C293 | C22×C4 |
| Frattini | C2 | C22×#11924078 |
| Fitting | C23×C293 | C4 |
| socle | C22×C293 | C2×C4 |
| hypercenter | C23 | #11924078 |
| hypocenter | C293 | C2×M16 |
| LCS | G ▷ C2×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ C23 | |
68 conjugacy classes of subgroups.
604 conjugacy classes — view the full character table.
| maximal subgroup of | #34037009, #34037010, C4×#17989811, … |
| maximal normal subgroup of | #34037009, #34037010, C4×#17989811, … |
| maximal quotient of | C2×#22627679, C4×#17989811, C2×C22⋊#14556880, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9376, 230);