#14514935

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂	C₂²⋊(A₅⋊C₄)
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×D₄	S₅
prime radical	C₂×#91881	C₂
cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

338 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 20 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

A minimal faithful permutation representation — 2 generators on 96 points:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240633);