Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128512 |
| Fitting | C2×H(5,𝔽2)×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#577 |
1460 conjugacy classes of subgroups.
1438 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35420314, #35420320, #35420341, … |
| maximal normal subgroup of | #35420314, #35420320, #35420341, … |
| maximal quotient of | C2×#24915989, C2×#24915993, C2×#24916056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19270);