Finite Group DatabasebetaFinite Group Databasebeta| order | 9376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C4×C293 ⋊ C2 |
| Sylow | C293 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D293 |
| commutator | C2×C293 | C22×C4 |
| Fitting | C4⋊C4×C293 | C2 |
| socle | C22×C293 | C23 |
| hypercenter | C4⋊C4 | D293 |
| hypocenter | C293 | C4×D4 |
| LCS | G ▷ C2×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,293|a^2=e,c^2=e,b^a=bd,f^b=f^292,f^c=f^2921480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34036209, #34036211, #34036214, … |
| maximal normal subgroup of | #34036209, #34036211, #34036214, … |
| maximal quotient of | #34035976, C4⋊C4×Dic293, #34036000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9376, 108);