Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C22×C4 |
| direct product | C101×#2789 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C101 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C101 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C101 ◁ G | |
352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12928 |
3232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×#12143, C101×#12237 |
| maximal normal subgroup of | C101×#12143, C101×#12237 |
| maximal quotient of | C101×#14400, C101×#14432, C101×#14462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 1521);