Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic53 |
| derived, Sylow | C53 ⋊ C4×C72 |
| Hall | C72×C53 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D53 |
| commutator, hypocenter | C53 | C4×C72 |
| Frattini | C2 | C72×D53 |
| Fitting, socle, prime radical | C2×C72×C53 | C2 |
| cosocle | C2×C53 | C2×C72 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C72 | |
60 conjugacy classes of subgroups.
2744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×ΓL(1,𝔽8)×Dic53, #3861×Dic53, #3862×Dic53, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)×Dic53, #3861×Dic53, #3862×Dic53, … |
| maximal quotient of | C72×Dic159, C3×C72×Dic53 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 13);