Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3482 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Frattini | C22 | C24×D83 |
| Fitting | C2×C4×Q8×C83 | C2 |
| hypercenter | C2×C4×Q8 | D83 |
| hypocenter | C83 | #3482 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×Q8 | |
1094 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=f,e^2=fg,b^a=bf,c^a=cg,d^b=df,h^b=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35371388, #35371394, #35371443, … |
| maximal normal subgroup of | #35371388, #35371394, #35371443, … |
| maximal quotient of | #35563864, #35563874, #35563879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18127);