Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #2029⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#2029⋊C3 |
| unambiguous semidirect product | #2029⋊C32 |
| unambiguous semidirect product | (C3×#2029)⋊C3 |
| Fitting | C3×#2029 ⋊ C3 |
| derived | #543 ⋊ C2×C32 |
| Sylow | #2029 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C3 | #120⋊C3 |
| commutator, cosocle, hypocenter | #543 | C2×C32 |
| Frattini | C24 | C2×C3×A4 |
| Fitting | C3×#2029 | C3 |
| LCS | G ▷ #543 | |
| UCS | C1 ◁ C22×C3 | |
358 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#14515304, C3×#11711443, C3×#11711413, … |
| maximal normal subgroup of | C3×#11711443, C3×#11711413, C3×#11710965 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153373);