Finite Group DatabasebetaFinite Group Databasebeta| order | 9212 |
| isoclinism | isoclinic class of D47 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic47 |
| unambiguous semidirect product | C47⋊(C4×C72) |
| derived, Sylow | C47 ⋊ C4×C72 |
| Hall | C72×C47 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D47 |
| commutator, hypocenter | C47 | C4×C72 |
| Frattini | C2 | C72×D47 |
| Fitting, socle | C2×C72×C47 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C2×C72 | |
60 conjugacy classes of subgroups.
2450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×ΓL(1,𝔽8)×Dic47, #3861×Dic47, #3862×Dic47, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)×Dic47, #3861×Dic47, #3862×Dic47, … |
| maximal quotient of | C72×Dic141, C3×C72×Dic47 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9212, 11);