Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C137 · Schur multiplier (H2) = C215 |
| direct product | C24×D4×C137 |
| unambiguous semidirect product | C4⋊(C25×C137) |
| unambiguous semidirect product | C22⋊(C25×C137) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C137 | C22 |
| commutator, Frattini, cosocle | C2 | C26×C137 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25×C137 ◁ G | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
10960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#1438×C137, C137×#13867, C137×#13902, … |
| maximal normal subgroup of | C2×#1438×C137, C137×#13867, C137×#13902, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2320);