Finite Group DatabasebetaFinite Group Databasebeta| order | 9376 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D2344 |
| Fitting | C2×C8×C293 ⋊ C2 |
| Sylow | C293 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D1172 |
| commutator | C4×C293 | C23 |
| Frattini | C4 | C22×D293 |
| Fitting | C2×C8×C293 | C2 |
| socle | C22×C293 | D4 |
| hypercenter | C2×C8 | D293 |
| hypocenter | C293 | C2×D8 |
| LCS | G ▷ C4×C293 ▷ C2×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
2350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34035929, #34035931, #34035941, … |
| maximal normal subgroup of | #34035929, #34035931, #34035941, … |
| maximal quotient of | C2×#22627546, C2×#22627558, C4×D2344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9376, 157);