Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C22 |
| direct product | C37×#2213 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C4×C8×C37 ◁ G | |
170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 592 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(39,42)(40,45)(41,43)(46,47)(48,53)(49,52)(50,51);(38,39,43,46,44,47,41,42)(40,45,51,53,49,52,48,50);(38,40)(39,45)(41,48)(42,50)(43,51)(44,49)(46,53)(47,52)851 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#12310, C37×#12311, C37×#12314, … |
| maximal normal subgroup of | C37×#12310, C37×#12311, C37×#12314, … |
| maximal quotient of | C37×#12418, C37×#12419, C37×#12424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 945);