Finite Group DatabasebetaFinite Group Databasebeta| order | 21756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
No aliases for this group.
| derived, Hall | C72×C37 ⋊ C3×C4 |
| Hall | C37×C7⋊Dic7 ⋊ C3 |
| Hall | C37⋊#3862 ⋊ C4 |
| Hall | C7⋊Dic7 ⋊ C37⋊C3 |
| Sylow | C72 ⋊ C4×C37⋊C3 |
| Sylow | C37 ⋊ #10596875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #24925954 |
| commutator, hypocenter | C72×C37 | C3×C4 |
| Fitting, socle, cosocle | C2×C72×C37 | C2×C3 |
| prime radical | C2×C37⋊#3862 | C2 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3108 |
Polycyclic presentation:
2,3,7^2,37,2|a^2=f,c^a=c^6,d^a=d^6,c^b=c^2,d^b=d^4,e^b=e^26652 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21756, 98);