Finite Group DatabasebetaFinite Group Databasebeta| order | 436 |
| isoclinism | isoclinic class of #89137 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C109 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C109 | C4 |
| prime radical, cosocle | D109 | C2 |
| LCS | G ▷ C109 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 109 |
A minimal faithful permutation representation — 2 generators on 109 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,87)(53,72,73,83)(57,76,74,79)(61,78,70,77)(65,80,81,75)(67,84,85,71)(82,92,93,91)(86,95,96,90)(88,94,98,89)(97,102,103,101)(99,104,105,100)(106,108,109,107);(1,2,5,10,19,32,49,70,60,43,28,41,58,77,91,101,107,109,105,98,87,76,51,30,46,65,82,94,84,63,42,25,12,3,7,14,23,36,53,74,56,39,26,15,24,37,54,75,90,100,103,96,85,66,83,72,47,67,86,97,104,95,80,59,38,21,8,16,27,40,57,73,52,35,22,13,6,11,20,33,50,71,89,93,81,64,45,62,79,68,88,99,106,108,102,92,78,55,34,17,29,44,61,69,48,31,18,9,4)Polycyclic presentation:
2^2,109|a^2=b,c^a=c^33,c^b=c^10831 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89137, #89137⋊C3, C3×#89137, … |
| maximal normal subgroup of | C2×#89137, #89137⋊C3, C3×#89137, … |
| maximal quotient of | #11724786, C2×#89137, C3×#89137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(436, 3);