Finite Group DatabasebetaFinite Group Databasebeta| order | 12016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D751 |
| unambiguous semidirect product | C23⋊D751 |
| Fitting | C23×C751 ⋊ C2 |
| Sylow | C751 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D751 |
| commutator, cosocle | C2×C751 | C23 |
| Frattini | C2 | C22×D751 |
| Fitting | C23×C751 | C2 |
| socle | C22×C751 | C22 |
| hypercenter | C23 | D751 |
| hypocenter | C751 | C2×D4 |
| LCS | G ▷ C2×C751 ▷ C751 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
3010 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37562352, (C22⋊D751)⋊C4, C4×C22⋊D751, … |
| maximal normal subgroup of | #37562352, (C22⋊D751)⋊C4, C4×C22⋊D751, … |
| maximal quotient of | C2×(C2×D751)⋊C4, C2×C22⋊Dic751, C2×Dic751⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12016, 35);