Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#13049549 |
| Sylow | C34 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10620215 |
| commutator, cosocle | C2×C34 | C25 |
| Frattini | C2 | C22×#10620215 |
| Fitting, socle | C23×C34 | C23 |
| hypocenter | C34 | C23×D4 |
| LCS | G ▷ C2×C34 ▷ C34 | |
| UCS | C1 ◁ C23 | |
21834 conjugacy classes of subgroups; only the 979 normal subgroups are shown.
This group has 21834 conjugacy classes of subgroups — too many to draw. Only its 979 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#72219698 |
| maximal normal subgroup of | C22×#72219698 |
Past the SmallGroups library coverage — no SmallGroups id.