Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #364×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2165 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556549 |
| commutator | C2×C4×C73 | C22×C4 |
| Frattini | C2×C8 | C22×D73 |
| Fitting | #364×C73 | C2 |
| socle | C2×C73 | #432 |
| hypercenter | #364 | D73 |
| hypocenter | C73 | #2165 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ #364 | |
128 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,e^b=eg,h^b=h^72,e^c=eg,h^c=h^721040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32996061, #32996063, #32996066, … |
| maximal normal subgroup of | #32996061, #32996063, #32996066, … |
| maximal quotient of | #33000997, #33001049, #33001320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6321);