Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C193 · Schur multiplier (H2) = C2×C4 |
| direct product | #486×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C193 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C193 |
| prime radical | #127×C193 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ C42×C193 ◁ G | |
118 conjugacy classes of subgroups.
4246 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1625×C193, #1626×C193, #1627×C193, … |
| maximal normal subgroup of | #1625×C193, #1626×C193, #1627×C193, … |
| maximal quotient of | #1834×C193, #1934×C193, #1957×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 167);