Finite Group DatabasebetaFinite Group Databasebeta| order | 23940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C3⋊#11716326 |
| unambiguous semidirect product | (C2×C3)⋊(C5×#11716326) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C3⋊#11716326 |
| commutator, cosocle, hypocenter | C3×C7×C19 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C7×C19 | C2×C3 |
| LCS | G ▷ C3×C7×C19 | |
| UCS | C1 ◁ C2×C5 | |
176 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3990 |
840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23940, 603);