Finite Group DatabasebetaFinite Group Databasebeta| order | 11504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C719 ⋊ C2 |
| Sylow | C719 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D719 |
| commutator, socle, cosocle | C2×C719 | C23 |
| Frattini | C2 | C22×D719 |
| Fitting | C2×C4×C719 | C2 |
| hypercenter | C2×C4 | D719 |
| hypocenter | C719 | #41 |
| LCS | G ▷ C2×C719 ▷ C719 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,719|c^2=d,b^a=bd,e^b=e^7182882 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37527520, #37527522, #37527600, … |
| maximal normal subgroup of | #37527520, #37527522, #37527600, … |
| maximal quotient of | #37527551, #37527553, C4×C22⋊D719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11504, 40);