Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C2×C42 |
| direct product | C101×#2835 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C101 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C101 |
| prime radical | C24×C101 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C101 ◁ G | |
380 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6464 |
2626 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×#12139, C101×#12233 |
| maximal normal subgroup of | C101×#12139, C101×#12233 |
| maximal quotient of | C101×#14627, C101×#14635, C101×#14647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 1567);