Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C23×Q8×D83 |
| Fitting | C23×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C24×Q8 |
6264 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1446×D83, #35326788, #35326791, … |
| maximal normal subgroup of | #1446×D83, #35326788, #35326791, … |
| maximal quotient of | C23×C4⋊C4×D83, C22×C4×Q8×D83, C23×#14581757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19304);