Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C193 · Schur multiplier (H2) = C25 |
| direct product | #576×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C193 | C22×D4 |
| commutator, Frattini, cosocle | C4 | C24×C193 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C193 ◁ #41×C193 ◁ G | |
268 conjugacy classes of subgroups.
4246 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2192×C193, #2194×C193 |
| maximal normal subgroup of | #2192×C193, #2194×C193 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 257);