Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D4×C521 ⋊ C2 |
| Sylow | C521 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D521 |
| commutator, socle, cosocle | C22×C521 | C23 |
| Fitting | C2×D4×C521 | C2 |
| hypercenter | C2×D4 | D521 |
| hypocenter | C521 | #121 |
| LCS | G ▷ C22×C521 ▷ C521 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8336 |
Polycyclic presentation:
2^5,521|b^2=d,b^a=bd,c^a=ce,f^c=f^5202614 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45687564, #45687569, #45687574, … |
| maximal normal subgroup of | #45687564, #45687569, #45687574, … |
| maximal quotient of | #45687289, #45687308, #45687320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 117);