Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D33×D175 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C11×C25 | C22 |
| Frattini | C5 | D33×D35 |
| socle | C3×C5×C7×C11 | C2×D5 |
| LCS | G ▷ C3×C7×C11×C25 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5775 |
1602 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 114);