Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C157 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#127×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C157 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C157 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C157 ◁ G | |
498 conjugacy classes of subgroups.
4396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#331×C157, #1545×C157, #1555×C157, … |
| maximal normal subgroup of | C2×#331×C157, #1545×C157, #1555×C157, … |
| maximal quotient of | C2×#384×C157, C2×#390×C157, C4×#127×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 211);