C₅₉×#7467 #28419576

order	15104
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#7467

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₅₉	D₄
commutator	C₄	C₄×C₁₆×C₅₉
Frattini, cosocle	C₂²×C₁₆	C₂²×C₅₉
socle	C₂²×C₅₉	C₄⋊C₁₆
prime radical	C₂³×C₅₉	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₅₉ ◁ C₂²×C₁₆×C₅₉ ◁ G

190 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 95
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 2 generators on 95 points:

(1,2)(3,4)(5,6,8,14,9,16,19,29,10,13,20,26,22,27,32,35,11,15,21,28,23,30,33,36,7,12,17,24,18,25,31,34)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(2,4)(6,12,15,13)(14,24,28,26)(16,25,30,27)(29,34,36,35)

Conjugacy classes & character table

6608 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 455);