Finite Group DatabasebetaFinite Group Databasebeta| order | 28028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C13 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C11×C13×C7⋊D7 |
| unambiguous semidirect product | (C2×C7)⋊(C11×C13×D7) |
| Fitting, socle | C2×C72×C11×C13 ⋊ C2 |
| derived, Sylow | C72 ⋊ C22×C11×C13 |
| Hall | C72×C11×C13 ⋊ C22 |
| Hall | C72×C13 ⋊ C22×C11 |
| Hall | C72×C11 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11×C13 | C7⋊D7 |
| commutator, cosocle, hypocenter | C72 | C22×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C11×C13 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C11×C13 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14014 |
7436 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28028, 83);