Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×Dic83 |
| Sylow | C83 ⋊ C22×C4×Q8 |
1664 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309832, #35309973, #391×Dic83, … |
| maximal normal subgroup of | #35309832, #35309973, #391×Dic83, … |
| maximal quotient of | C22×C4⋊C4×Dic83, C2×C4×Q8×Dic83, C22×#19127587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17686);