#14514975

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₄	D₄×A₅
commutator	#6732	C₂×C₄
Frattini, cosocle	C₂×C₄	C₂²×A₅
Fitting, hypercenter	#108	A₅
socle	C₂	C₄⋊C₄×A₅
prime radical	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

224 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 23 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) = 96
transitive degree	μ_t(G) = 96

Permutation generators:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240673);