Finite Group DatabasebetaFinite Group Databasebeta| order | 9904 |
| automorphism | Aut(G) order 12241344 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4952 |
| Fitting | C8×C619 ⋊ C2 |
| Sylow | C619 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D2476 |
| commutator, cosocle | C4×C619 | C22 |
| Frattini | C4 | C2×D619 |
| Fitting | C8×C619 | C2 |
| socle | C2×C619 | D4 |
| hypercenter | C8 | D619 |
| hypocenter | C619 | D8 |
| LCS | G ▷ C4×C619 ▷ C2×C619 ▷ C619 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,619|c^2=d,b^a=bc,c^a=cd,e^a=e^618,c^b=cd,e^b=e^6182479 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34090294, D9904, #34090296, … |
| maximal normal subgroup of | #34090294, D9904, #34090296, … |
| maximal quotient of | #34090275, #34090287, D9904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9904, 26);