#14514934

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×Q₈	S₅
prime radical	C₂×#91883	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×Q₈

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

normal subgroups only

This group has 344 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:

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

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, 240632);