Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8257536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C8×C193 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C24×C193 |
| socle, prime radical | C24×C193 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
338 conjugacy classes of subgroups.
12352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#336×C193, #1729×C193, C2×#340×C193, … |
| maximal normal subgroup of | C2×#336×C193, #1729×C193, C2×#340×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 246);