Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C7 |
| direct product | C13×D15×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D15×C7⋊D7 |
| commutator, cosocle, hypocenter | C3×C5×C72 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C13 | C22 |
| LCS | G ▷ C3×C5×C72 | |
| UCS | C1 ◁ C13 | |
400 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 9555 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(4,5,7,8,6)(10,11)(12,13)(14,15)(17,18)(19,20)(21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35);(2,3)(5,6)(7,8)(16,17,19,21,22,20,18);(9,10,12,14,15,13,11)3042 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 1133);