Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5×C11 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C112 ⋊ C4 |
| Sylow | C112 ⋊ #1039 |
| Sylow | C52 ⋊ #92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C112 | C4 |
| prime radical, cosocle | C52×C11⋊D11 | C2 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,11^2|a^2=b,c^a=c^4,d^a=d^4,e^a=e^8f^7,f^a=e^8f^3,e^b=e^10,f^b=f^10778 conjugacy classes — view the full character table.
| maximal subgroup of | #49137555, #49137557, #49137612, … |
| maximal normal subgroup of | #49137555, #49137557, #49137613, … |
| maximal quotient of | C3×#27130990, C3⋊#27130990 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 269);