Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C193 · Schur multiplier (H2) = C22 |
| direct product | #401×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C193 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C193 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C193 ◁ G | |
118 conjugacy classes of subgroups.
4246 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#401×C193, #2401×C193 |
| maximal normal subgroup of | C2×#401×C193, #2401×C193 |
| maximal quotient of | #1443×C193, #2104×C193, C2×#401×C193 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 82);