Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C157 ⋊ C2 |
| Sylow | C157 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D157 |
| commutator, socle | C2×C157 | C22×C8 |
| Fitting | M32×C157 | C2 |
| prime radical | #14578954 | C4 |
| cosocle | C8×C157 | C23 |
| hypercenter | M32 | D157 |
| hypocenter | C157 | #504 |
| LCS | G ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,d^2=e,e^2=f,g^a=g^156,c^b=cf,g^c=g^1561600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34101970, #34101972, #34101975, … |
| maximal normal subgroup of | #34101970, #34101972, #34101975, … |
| maximal quotient of | #34101734, #34101735, #34101748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 967);