Finite Group DatabasebetaFinite Group Databasebeta| order | 9376 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#11924078)⋊C4 |
| Fitting | C2×C4×C293 ⋊ C4 |
| Sylow | C293 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#11924078 |
| commutator | C2×C293 | C42 |
| Fitting | C2×C4×C293 | C4 |
| socle | C22×C293 | C2×C4 |
| hypercenter | C2×C4 | #11924078 |
| hypocenter | C293 | #95 |
| LCS | G ▷ C2×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,293|a^2=d,b^2=e,b^a=bc,f^a=f^138,f^d=f^292604 conjugacy classes — view the full character table.
| maximal subgroup of | #34036980, #34036981, #34036982, … |
| maximal normal subgroup of | #34036980, #34036981, #34036982, … |
| maximal quotient of | (C2×#11924078)⋊C8, #34036995, #34036996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9376, 197);