Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#14581838 |
| Fitting | C4×#41×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups.
1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295801, #35295804, #35370782, … |
| maximal normal subgroup of | #35295801, #35295804, #35370782, … |
| maximal quotient of | C4×#19128173, C4×#19128175, C4×#19128181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17717);