Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C193 · Schur multiplier (H2) = C22 |
| direct product | #436×C193 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C193 | C23 |
| commutator | C22 | C22×C4×C193 |
| Frattini, cosocle | C2×C4 | C23×C193 |
| socle | C22×C193 | C22×C4 |
| prime radical | C2×D4×C193 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C193 ◁ G | |
122 conjugacy classes of subgroups.
5404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1330×C193, #1581×C193, #1583×C193, … |
| maximal normal subgroup of | #1330×C193, #1581×C193, #1583×C193, … |
| maximal quotient of | #1589×C193, #1590×C193, #1591×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 117);