Finite Group DatabasebetaFinite Group Databasebeta| order | 9664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#41×C151 ⋊ C2 |
| Sylow | C151 ⋊ #546 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D151 |
| commutator, socle, cosocle | C22×C151 | C24 |
| Fitting | C2×#41×C151 | C2 |
| hypercenter | C2×#41 | D151 |
| hypocenter | C151 | #546 |
| LCS | G ▷ C22×C151 ▷ C151 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,151|a^2=e,b^a=be,c^a=cf,d^b=de,g^c=g^1501525 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34080584, #34080593, #34080614, … |
| maximal normal subgroup of | #34080584, #34080593, #34080614, … |
| maximal quotient of | D4×(C2×D151)⋊C4, #34071940, #34071960, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9664, 1187);