Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #126×C149 ⋊ C2 |
| Sylow | C149 ⋊ #538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D149 |
| commutator, socle, cosocle | C22×C149 | C24 |
| Fitting | #126×C149 | C2 |
| hypercenter | #126 | D149 |
| hypocenter | C149 | #538 |
| LCS | G ▷ C22×C149 ▷ C149 | |
| UCS | C1 ◁ C22 ◁ #126 | |
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,149|b^2=f,b^a=be,c^a=cf,d^a=de,g^a=g^148,c^b=ce,g^d=g^1481058 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #538×D149, C2×#23750214, #34058074, … |
| maximal normal subgroup of | #538×D149, C2×#23750214, #34058074, … |
| maximal quotient of | #34047285, #34047322, #34047323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 1138);