Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#2193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C11×#131 ◁ G | |
210 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,19)(14,23)(15,26)(16,17)(20,34)(21,38)(22,33)(24,40)(25,30)(27,31)(28,29)(32,35)(36,43)(37,41);(12,13)(14,20)(15,27)(16,21)(17,31)(18,22)(19,26)(23,35)(24,41)(25,37)(28,33)(29,38)(30,36)(32,39)(34,40)(42,43);(12,14,18,25)(13,20,22,37)(15,24,29,40)(16,30,17,23)(19,32,33,43)(21,36,31,35)(26,39,28,42)(27,41,38,34)253 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 925);