Finite Group DatabasebetaFinite Group Databasebeta| order | 8379 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#89204 |
| derived, Sylow | C72 ⋊ C9×C19 |
| Hall | C72×C19 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | #3861 |
| commutator, hypocenter | C72 | C9×C19 |
| Frattini | C3 | C19×#3861 |
| Fitting, socle | C3×C72×C19 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C19 | |
60 conjugacy classes of subgroups.
1083 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#11725077, #30660576, C19×#11725076, … |
| maximal normal subgroup of | C19×#11725077, #30660576, C19×#11725076, … |
| maximal quotient of | C2×C19×#89204, C19×C22⋊#89204 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8379, 20);