Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3144758722560 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C215 |
| abelian | C26×C157 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5650 conjugacy classes of subgroups.
10048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#379×C157, #2846×C157, C23×C22⋊C4×C157, … |
| maximal normal subgroup of | C2×#379×C157, #2846×C157, C23×C22⋊C4×C157, … |
| maximal quotient of | C25×C4×C157, C24×D4×C157, C24×Q8×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 267);