Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×#11763982 |
| Fitting, socle | C3×C72×C13 ⋊ C3×C4 |
| derived | C7×C13 ⋊ C32×C4×C7 |
| Hall | C3×C7×#63270 ⋊ C4 |
| Hall | C72×#261 ⋊ C32 |
| Hall | C72×C13 ⋊ C32×C4 |
| Hall | #261 ⋊ C3×C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C3×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×C4×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #11763982 |
| commutator, hypocenter | C7×C13 | C32×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C3×C4 |
| prime radical | C3×C7×#10587716 | C2 |
| cosocle | C7×D13 | C2×C32×C7 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C7 | |
168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 819 |
567 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 987);