Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#19127723 |
| Fitting | C2×C4⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#423 |
576 conjugacy classes of subgroups.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35293868, #35293874, #35293878, … |
| maximal normal subgroup of | #35293868, #35293874, #35293878, … |
| maximal quotient of | C2×#24906217, C2×#24906220, C2×#24906223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13063);