Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊C4×C433 ⋊ C2 |
| Sylow | C433 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D433 |
| commutator, socle, cosocle | C22×C433 | C23 |
| Fitting | C22⋊C4×C433 | C2 |
| hypercenter | C22⋊C4 | D433 |
| hypocenter | C433 | #120 |
| LCS | G ▷ C22×C433 ▷ C433 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3464 |
Polycyclic presentation:
2^5,433|b^a=bd,c^a=ce,f^a=f^432,f^c=f^4322174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #42121999, #120×D433, C2×#28357190, … |
| maximal normal subgroup of | #42121999, #120×D433, C2×#28357190, … |
| maximal quotient of | #42121666, #42121685, #42121686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 116);