Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2372 |
560 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=eg,c^2=e,d^2=f,b^a=be,c^a=cf,d^b=de,h^c=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2372×D83, C2×#24910571, #35564100, … |
| maximal normal subgroup of | #2372×D83, C2×#24910571, #35564100, … |
| maximal quotient of | #35325854, #35325932, #35325934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7618);