Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#92262 |
| Fitting | C2×C9⋊H(3,𝔽3) ⋊ C2 |
| Sylow | C9⋊H(3,𝔽3) ⋊ C22 |
191 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #92262⋊C4, #14516817, #14516818, … |
| maximal normal subgroup of | #92262⋊C4, #14516817, #14516818, … |
| maximal quotient of | #14517320, C4×#92262, C4⋊#92262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 608);