Finite Group DatabasebetaFinite Group Databasebeta| order | 13696 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C107 · Schur multiplier (H2) = C24×C4 |
| direct product | C107×#2273 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C107 | C24 |
| commutator | C2 | C22×C42×C107 |
| Frattini, cosocle | C23 | C24×C107 |
| prime radical | C25×C107 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C107 ◁ G | |
912 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3424 |
7276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C107×#8734, C107×#9407, C107×#9409, … |
| maximal normal subgroup of | C107×#8734, C107×#9407, C107×#9409, … |
| maximal quotient of | C107×#13749, C107×#13775, C107×#13778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13696, 1005);