Finite Group DatabasebetaFinite Group Databasebeta| order | 484 |
| isoclinism | isoclinic class of #92150 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C112 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112 | C4 |
| prime radical, cosocle | C11⋊D11 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 22 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2)(3,6,7,16)(4,9,10,17)(5,13,14,8)(11,18,12,19)(15,21,20,22);(1,3,8,17,22,18,19,21,9,13,7)(2,11,6,20,5,10,4,14,15,16,12)Polycyclic presentation:
2^2,11^2|a^2=b,c^a=c^8d^5,d^a=c^9d^3,c^b=c^10,d^b=d^1034 conjugacy classes — view the full character table.
| derived subgroup of | #11757261⋊C2 |
| maximal subgroup of | #11757261, #92150⋊C2, #11757263, … |
| maximal normal subgroup of | #11757261, #92150⋊C2, #11757263, … |
| maximal quotient of | #11757242, C2×#92150, C3×#92150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(484, 8);