Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C157 · Schur multiplier (H2) = C24 |
| direct product | Q82×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C157 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C157 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C157 ◁ G | |
212 conjugacy classes of subgroups.
3925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1623×C157, #1633×C157, #1645×C157, … |
| maximal normal subgroup of | #1623×C157, #1633×C157, #1645×C157, … |
| maximal quotient of | Q8×C4⋊C4×C157, #2369×C157, #2451×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 239);