Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M64×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D83 |
| commutator, socle | C2×C83 | C22×C16 |
| Fitting | M64×C83 | C2 |
| prime radical | #13050590 | C8 |
| cosocle | C16×C83 | C23 |
| hypercenter | M64 | D83 |
| hypocenter | C83 | #2258 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C16 ◁ M64 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^82,c^b=cg,h^c=h^821720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35324965, #35324967, #35324970, … |
| maximal normal subgroup of | #35324965, #35324967, #35324970, … |
| maximal quotient of | #35324585, #35324586, #35324599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6805);