Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C193 · Schur multiplier (H2) = C25 |
| direct product | C22×M16×C193 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C193 | C22 |
| commutator | C2 | C23×C4×C193 |
| Frattini, cosocle | C4 | C24×C193 |
| socle | C23×C193 | C2×C4 |
| prime radical | C24×C193 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C193 ◁ G | |
298 conjugacy classes of subgroups.
7720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1728×C193, #1729×C193, C2×H(3,ℤ/4)×C193, … |
| maximal normal subgroup of | #1728×C193, #1729×C193, C2×H(3,ℤ/4)×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 247);