Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #117×C73 ⋊ C4 |
| Sylow | C73 ⋊ #2298 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Frattini | C22 | C23×#64408 |
| Fitting | #117×C73 | C4 |
| hypercenter | #117 | #64408 |
| hypocenter | C73 | #2298 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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=g,b^2=g,c^2=e,d^2=f,b^a=be,c^a=cf,h^a=h^46,h^b=h^27,h^g=h^72416 conjugacy classes — view the full character table.
| maximal subgroup of | #34020350, #34020353, #34020354, … |
| maximal normal subgroup of | #34020350, #34020353, #34020354, … |
| maximal quotient of | #34014592, #34014597, #34014600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20972);