Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C157 ⋊ #557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D157 |
| commutator, socle, prime radical, cosocle | C22×C157 | C24 |
| Fitting | C4×Q8×C157 | C2 |
| hypercenter | C4×Q8 | D157 |
| hypocenter | C157 | #557 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
200 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=f,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,g^a=g^156,d^b=de1585 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34099231, #34099235, #34099293, … |
| maximal normal subgroup of | #34099231, #34099235, #34099293, … |
| maximal quotient of | Q8×C4⋊Dic157, #34103054, #34103091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1278);