Finite Group DatabasebetaFinite Group Databasebeta| order | 6152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D769 |
| unambiguous semidirect product | C769⋊C23 |
| unambiguous semidirect product | (C2×C769)⋊C22 |
| Fitting, socle | C22×C769 ⋊ C2 |
| derived, Sylow | C769 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D769 |
| commutator, hypocenter | C769 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C769 | C2 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
1544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27134358, C2×C4×D769, D4×D769, … |
| maximal normal subgroup of | #27134358, C2×C4×D769, D4×D769, … |
| maximal quotient of | C2×C4×D769, C22×Dic769, D4×D769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6152, 12);