Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C193 · Schur multiplier (H2) = C24 |
| direct product | #562×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C193 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C193 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ G | |
220 conjugacy classes of subgroups.
3667 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1656×C193, #1661×C193, #1662×C193 |
| maximal normal subgroup of | #1656×C193, #1661×C193, #1662×C193 |
| maximal quotient of | #2376×C193, #2377×C193, #2378×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 243);