Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of A4×#1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | A4×#1113 |
| Fitting, socle, derived | C22×C33 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C33 | C22×C3 |
| LCS | G ▷ C22×C33 | |
| UCS | C1 | |
526 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #72220699, D33×A4, S4×#1113, … |
| maximal normal subgroup of | D33×A4, S4×#1113, #72220997 |
| maximal quotient of | #72220699, A4×#89101 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3556);