Finite Group DatabasebetaFinite Group Databasebeta| order | 13792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C431 ⋊ C2 |
| Sylow | C431 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D431 |
| commutator, socle, cosocle | C22×C431 | C23 |
| Fitting | C4⋊C4×C431 | C2 |
| prime radical | C22×D431 | C22 |
| hypercenter | C4⋊C4 | D431 |
| hypocenter | C431 | C22⋊Q8 |
| LCS | G ▷ C22×C431 ▷ C431 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6896 |
Polycyclic presentation:
2^5,431|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^430,f^c=f^4302164 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D431, C2×#28352167, #42119567, … |
| maximal normal subgroup of | C22⋊Q8×D431, C2×#28352167, #42119567, … |
| maximal quotient of | #42118918, #42118930, #42118933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13792, 124);