Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C433 ⋊ C2 |
| Sylow | C433 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D433 |
| commutator, socle, cosocle | C22×C433 | C23 |
| Fitting | C4⋊C4×C433 | C2 |
| prime radical | C22×D433 | C22 |
| hypercenter | C4⋊C4 | D433 |
| hypocenter | C433 | C22⋊Q8 |
| LCS | G ▷ C22×C433 ▷ C433 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6928 |
Polycyclic presentation:
2^5,433|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^432,f^c=f^4322174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D433, C2×#28357198, #42122319, … |
| maximal normal subgroup of | C22⋊Q8×D433, C2×#28357198, #42122319, … |
| maximal quotient of | #42121670, #42121682, #42121685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 124);