Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C7 |
| direct product | C37×#10596875 |
| derived, Sylow | C72 ⋊ C3×C4×C37 |
| Hall | C37×C7⋊Dic7 ⋊ C3 |
| Hall | C37×#3862 ⋊ C4 |
| Hall | C72×C37 ⋊ C3×C4 |
| Hall | C7⋊Dic7 ⋊ C3×C37 |
| Hall | #3862 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | #64425 |
| commutator, hypocenter | C72 | C3×C4×C37 |
| Frattini | C2 | C37×#64425 |
| Fitting, socle | C2×C72×C37 | C2×C3 |
| prime radical | C2×C37×#3862 | C2 |
| cosocle | C2×C72 | C2×C3×C37 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C37 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3108 |
1036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 96);