Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C149 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10597010 |
| commutator, hypocenter | C149 | C4×C16 |
| Frattini | C2×C4 | C2×#10597010 |
| Fitting | C2×C8×C149 | C4 |
| socle, prime radical | C22×C149 | C2×C8 |
| cosocle | C2×#11924746 | C22 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,149|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^105,g^b=g^148,g^c=g^148656 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11924753, #34059602, #11924753⋊C16, … |
| maximal normal subgroup of | C16×#11924753, #34059602, #11924753⋊C16, … |
| maximal quotient of | C8×#14558739, #34059606, #34059730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 1435);