Finite Group DatabasebetaFinite Group Databasebeta| order | 26852 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×#10587739 |
| Fitting, socle, Hall | C72×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C4×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | #10587739 |
| commutator, hypocenter | C137 | C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C137 | C4 |
| prime radical | C72×D137 | C2 |
| cosocle | D137 | C2×C72 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C72 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6713 |
1862 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26852, 22);