Finite Group DatabasebetaFinite Group Databasebeta| order | 12016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C751 ⋊ C2 |
| Sylow | C751 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D751 |
| commutator, socle, cosocle | C2×C751 | C23 |
| Fitting | Q8×C751 | C2 |
| hypercenter | Q8 | D751 |
| hypocenter | C751 | #41 |
| LCS | G ▷ C2×C751 ▷ C751 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,751|c^2=d,b^a=bd,e^a=e^750,e^b=e^750,e^c=e^7501885 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37562459, #37562461, #37562465, … |
| maximal normal subgroup of | #37562459, #37562461, #37562465, … |
| maximal quotient of | #37562396, #37562400, Q8×Dic751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12016, 41);