Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×D4×Dic83 |
| Sylow | C83 ⋊ C42×D4 |
924 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×Dic83, #35295008, #35295018, … |
| maximal normal subgroup of | D4⋊C8×Dic83, #35295008, #35295018, … |
| maximal quotient of | C4×C22⋊C4×Dic83, C4×C4⋊C4×Dic83, C4×#19127581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6857);