Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C193 · Schur multiplier (H2) = C29 |
| direct product | C2×H(5,𝔽2)×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C193 | C24 |
| commutator, Frattini, cosocle | C2 | C25×C193 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ G | |
898 conjugacy classes of subgroups.
6562 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1790×C193, #1792×C193, #1795×C193 |
| maximal normal subgroup of | #1790×C193, #1792×C193, #1795×C193 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 264);