Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×#13050590 |
| Fitting | C22×C42×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C4×#41 |
1728 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295778, #35295781, #35309810, … |
| maximal normal subgroup of | #35295778, #35295781, #35309810, … |
| maximal quotient of | C2×C4×#14581751, C2×C4×#14581749, C2×C42×C22⋊D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17690);