Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C193 · Schur multiplier (H2) = C23 |
| direct product | C2×#106×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C193 | D4 |
| commutator | C4 | C22×C4×C193 |
| Frattini, cosocle | C2×C4 | C23×C193 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C193 ◁ C22×C4×C193 ◁ G | |
130 conjugacy classes of subgroups.
5404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1383×C193, #1386×C193, C4×#106×C193, … |
| maximal normal subgroup of | #1383×C193, #1386×C193, C4×#106×C193, … |
| maximal quotient of | C2×#334×C193, #1566×C193, #1570×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 106);