Finite Group DatabasebetaFinite Group Databasebeta| order | 10352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic647 |
| derived, Sylow | C647 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D647 |
| commutator, hypocenter | C647 | C22×C4 |
| Frattini | C2 | C22×D647 |
| Fitting, socle, prime radical | C23×C647 | C2 |
| cosocle | C2×C647 | C23 |
| LCS | G ▷ C647 | |
| UCS | C1 ◁ C23 | |
54 conjugacy classes of subgroups.
2600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C647⋊#95, C2×C4×Dic647, C2×(C2×D647)⋊C4, … |
| maximal normal subgroup of | C647⋊#95, C2×C4×Dic647, C2×(C2×D647)⋊C4, … |
| maximal quotient of | C2×C4×Dic647, C2×C22⋊Dic647, C2×C4⋊Dic647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10352, 33);