Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C193 · Schur multiplier (H2) = C23 |
| direct product | #450×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C193 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C193 |
| prime radical | C22×D4×C193 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ C22×C4×C193 ◁ G | |
188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3667 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1596×C193, #1597×C193, #1599×C193, … |
| maximal normal subgroup of | #1596×C193, #1597×C193, #1599×C193, … |
| maximal quotient of | #1601×C193, #1604×C193, #1613×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 131);