Finite Group DatabasebetaFinite Group Databasebeta| order | 9376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C293 ⋊ C2 |
| Sylow | C293 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D293 |
| commutator, socle | C2×C293 | C22×C4 |
| Fitting | M16×C293 | C2 |
| hypercenter | M16 | D293 |
| hypocenter | C293 | #131 |
| LCS | G ▷ C2×C293 ▷ C293 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,293|a^2=d,d^2=e,f^a=f^292,c^b=ce,f^c=f^2921480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34036243, #34036245, #34036248, … |
| maximal normal subgroup of | #34036243, #34036245, #34036248, … |
| maximal quotient of | #34036086, #34036087, #34036094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9376, 154);