Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C83 ⋊ #3504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | C4×#41×C83 | C2 |
| prime radical | C2×#41×C83 | C22 |
| hypercenter | C4×#41 | D83 |
| hypocenter | C83 | #3504 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=g,c^2=fg,e^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^82,d^b=df1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296669, #35372651, #35372678, … |
| maximal normal subgroup of | #35296669, #35372651, #35372678, … |
| maximal quotient of | #35564515, #35564864, #35564884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18336);