#14514915

order	1920
automorphism	?
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, Fitting, hypercenter	C₁₆	S₅
commutator, hypocenter	SL(2,𝔽₅)	C₁₆
socle	C₂	A₅⋊C₁₆
prime radical	#6732	C₈
cosocle	#11746446	C₂
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₁₆

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 192
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 2 generators on 192 points:

(1,111,44,190,32,125,46,113,3,173,62,129,49,184,66,177,11,105,19,133,68,172,61,108,23,163,36,176,10,182,18,109,38,146,31,128,22,170,43,149,2,158,4,112,45,192,60,107,7,140,15,175,63,157,75,99,17,189,30,106,21,162,88,148,34,127,48,164,37,188,29,98,6,132,67,147,33,156,47,134,13,174,9,159,5,139,74,120,12,126,20,141,16,187,86,130)(8,165,50,153,65,171,82,131,53,180,69,117,85,186,96,123,35,144,55,137,79,179,90,102,59,168,93,122,41,143,54,110,52,152,72,101,58,183,92,104,14,116,25,166,51,178,87,97,28,160,78,181,70,142,95,135,24,151,64,145,57,167,91,155,39,115,84,169,94,150,71,119,27,136,77,154,73,114,83,138,81,121,40,118,26,185,76,124,42,100,56,161,80,191,89,103);(1,154,76,160,21,104,78,186,23,153,96,136,5,155,77,183,7,122,92,165,49,124,50,167,6,181,91,168,22,123,93,185)(2,175,66,115,32,177,67,143,34,147,43,100,10,149,44,142,12,190,88,144,63,148,36,114,11,176,74,116,33,120,15,171)(3,145,86,173,37,102,30,188,38,118,61,146,16,97,9,187,17,117,60,189,68,119,62,172,13,101,29,174,45,103,31,192)(4,179,52,161,46,121,80,135,48,178,24,137,18,180,79,138,20,150,81,166,75,152,51,131,19,191,53,169,47,151,94,110)(8,164,83,140,57,109,25,184,59,141,82,132,26,99,84,170,28,133,54,111,85,134,56,162,27,112,95,163,58,113,55,139)(14,159,71,105,65,107,72,156,39,129,89,158,41,98,64,125,42,128,90,127,70,130,40,182,35,106,87,126,73,108,69,157)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240613);