Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | C7×#63271⋊A4 |
| unambiguous semidirect product | #63271⋊(C7×A4) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #63271⋊A4 |
| commutator, cosocle, hypocenter | C22×C7×C13 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C13 | C32 |
| LCS | G ▷ C22×C7×C13 | |
| UCS | C1 ◁ C7 | |
132 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 132 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) = 1092 |
476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1338);