Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | H(3,𝔽4)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3540 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | H(3,𝔽4)×C83 | C2 |
| hypercenter | H(3,𝔽4) | D83 |
| hypocenter | C83 | #3540 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
1058 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=f,c^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,h^b=h^82,h^c=h^82,h^e=h^82817 conjugacy classes — view the full character table.
| maximal subgroup of | #35558500, #3540×D83, C2×#24921736, … |
| maximal normal subgroup of | #35558500, #3540×D83, C2×#24921736, … |
| maximal quotient of | #35567183, #35567536, #35567852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18783);