Finite Group DatabasebetaFinite Group Databasebeta| order | 9212 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C47⋊#5997 |
| Fitting, socle, derived, Hall | C72×C47 ⋊ C4 |
| Sylow | C72 ⋊ Dic47 |
| Sylow | C47 ⋊ #5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C47 | C4 |
| LCS | G ▷ C72×C47 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7^2,47|a^2=b,c^a=c^4d^6,d^a=c^3d^3,e^a=e^46,c^b=c^6,d^b=d^6614 conjugacy classes — view the full character table.
| maximal subgroup of | C47⋊#10596885, C47⋊(#5997⋊C3), C3×C47⋊#5997, … |
| maximal normal subgroup of | C47⋊(#5997⋊C3), C3×C47⋊#5997 |
| maximal quotient of | C3×C47⋊#5997, C3⋊(C47⋊#5997) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9212, 23);