Finite Group DatabasebetaFinite Group Databasebeta| order | 5684 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic29 |
| derived, Sylow | C29 ⋊ C4×C72 |
| Hall | C72×C29 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D29 |
| commutator, hypocenter | C29 | C4×C72 |
| Frattini | C2 | C72×D29 |
| Fitting, socle | C2×C72×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C72 | |
60 conjugacy classes of subgroups.
1568 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×ΓL(1,𝔽8)×Dic29, Dic29×#3861, Dic29×#3862, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)×Dic29, Dic29×#3861, Dic29×#3862, … |
| maximal quotient of | C3×C72×Dic29, C72×Dic87, C72×Dic145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5684, 22);