Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q16×D83 |
| Fitting | C4×Q16×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1332×D83, #35314155, #1334×D83, … |
| maximal normal subgroup of | #1332×D83, #35314155, #1334×D83, … |
| maximal quotient of | C8×Q16×D83, #1584×D83, #1591×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13271);