C₅₉×#12389 #28424498

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#12389

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
prime radical	C₂×D₈×C₅₉	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₅₉×#446 ◁ G

284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 107
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 3 generators on 107 points:

(1,2,5,8)(3,9,10,16)(4,12,13,7)(6,14,15,11)(17,18,22,26)(19,27,29,45)(20,31,33,47)(21,36,34,25)(23,38,39,28)(24,41,43,35)(30,46,37,42)(32,44,48,40)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(4,13)(7,12)(9,16)(11,14)(17,19)(18,23)(20,32)(21,37)(22,29)(24,42)(25,44)(26,39)(27,31)(28,35)(30,34)(33,48)(36,40)(38,41)(43,46)(45,47);(1,3,5,10)(2,6,8,15)(4,14,13,11)(7,16,12,9)(20,33)(24,43)(27,45)(28,38)(31,47)(32,48)(35,41)(42,46)

Conjugacy classes & character table

1829 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5377);