Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#14581816 |
| Fitting | C4×D8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14581816, #35373821, #35373835, … |
| maximal normal subgroup of | C8×#14581816, #35373821, #35373835, … |
| maximal quotient of | C8×#14581816, #35373982, #35374004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13313);