Finite Group DatabasebetaFinite Group Databasebeta| order | 19328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C24×C4 |
| direct product | #2631×C151 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C151 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C151 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C151 ◁ G | |
628 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9664 |
4832 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C151×#9187, C151×#10018, C151×#10022, … |
| maximal normal subgroup of | C151×#9187, C151×#10018, C151×#10022, … |
| maximal quotient of | C151×#14267, C151×#14288, C151×#14298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 1363);