Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #126×C157 ⋊ C2 |
| Sylow | C157 ⋊ #552 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D157 |
| commutator, socle, cosocle | C22×C157 | C24 |
| Fitting | #126×C157 | C2 |
| prime radical | C2×C22⋊D157 | C22 |
| hypercenter | #126 | D157 |
| hypocenter | C157 | #552 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ #126 | |
214 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,157|a^2=e,b^2=f,c^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^156,g^d=g^1561117 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #552×D157, C2×#23757959, #34113688, … |
| maximal normal subgroup of | #552×D157, C2×#23757959, #34113688, … |
| maximal quotient of | #34102993, #34102995, #34103002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1235);