#91883

order	480
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

derived

SL(2,𝔽₅) ⋊ C₂²

Subgroups

	subgroup	G/H
center, Frattini, socle, cosocle	C₂	C₂²×A₅
commutator, hypocenter	SL(2,𝔽₅)	C₂²
Fitting, hypercenter	Q₈	A₅
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ Q₈

85 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:

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

Conjugacy classes & character table

24 conjugacy classes — view the full character table.

Relationships

derived subgroup of	SL(2,𝔽₅)⋊A₄, #72276703, #72276752, …
maximal subgroup of	#11751524, #11751525, #11751547, …
maximal normal subgroup of	#11751524, #11751525, #11751547, …
maximal quotient of	C₄⋊#6732, #11751539, Q₈×SL(2,𝔽₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 959);