C₄×C₁₉×#376 #18019705

order	4864
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄³×C₁₉ · Schur multiplier (H₂) = C₂²×C₄⁴

Aliases

direct product

C₄×C₁₉×#376

Subgroups

	subgroup	G/H
center	C₂²×C₄²×C₁₉	C₂²
commutator	C₂	C₂×C₄³×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
socle, prime radical	C₂⁴×C₁₉	C₂⁴
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄²×C₁₉ ◁ G

2302 conjugacy classes of subgroups; only the 1534 normal subgroups are shown.

normal subgroups only

This group has 2302 conjugacy classes of subgroups — too many to draw. Only its 1534 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(5,6,7,8)(13,14)(15,18)(16,17)(19,20);(9,10,11,12)(14,17)(18,20);(13,15,16,19)(14,18,17,20)

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6734);