Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2468 |
532 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=e,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=cg1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2468×D83, C2×#24911529, #35572577, … |
| maximal normal subgroup of | #2468×D83, C2×#24911529, #35572577, … |
| maximal quotient of | #35326526, #35326691, #35327346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 8576);