#91145

order	480
isoclinism	isoclinic class of SL(2,𝔽₅)
automorphism	Aut(G) = C₂²×S₅ (order 480) · Inn(G) = A₅ · Out(G) = C₂³
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Fitting, hypercenter	C₈	A₅
commutator, hypocenter	SL(2,𝔽₅)	C₄
Frattini, cosocle	C₄	C₂×A₅
socle	C₂	C₄×A₅
prime radical	#6732	C₂
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₈

43 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 48 points:

(1,7,12,5,20,25,6,21,30,17,38,28)(2,34,3,9,35,11,10,46,14,24,18,27)(4,19,29,15,36,40,16,37,43,32,47,42)(8,44,13,22,45,26,23,48,31,39,33,41);(1,37,9,26,25,16,20,39,3,42,5,47,10,31,30,32,21,8,11,29,6,19,24,41,28,4,38,22,14,40,17,36,2,13,12,15,7,23,27,43)(18,33,34,44,35,45,46,48)

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

derived subgroup of	#14515013, #14515014, #14515015, …
maximal subgroup of	#11746443, #11746446, #11751490, …
maximal normal subgroup of	#11746443, #11746446, #11751490, …
maximal quotient of	C₈×SL(2,𝔽₅), C₂×#91145, C₃⋊#91145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 221);