C₄×C₅₉×#376 #28425855

order	15104
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄³×C₅₉ · Schur multiplier (H₂) = C₂²×C₄⁴

Aliases

direct product

C₄×C₅₉×#376

Subgroups

	subgroup	G/H
center	C₂²×C₄²×C₅₉	C₂²
commutator	C₂	C₂×C₄³×C₅₉
Frattini, cosocle	C₂⁴	C₂⁴×C₅₉
socle, prime radical	C₂⁴×C₅₉	C₂⁴
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄²×C₅₉ ◁ 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) = 79
transitive degree	μ_t(G) = 15104

A minimal faithful permutation representation — 4 generators on 79 points:

(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79);(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

9440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6734);