#91290

order	480
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

Hall	C₃×C₅ ⋊ #131
Sylow	C₅ ⋊ #901
Sylow	C₃ ⋊ #4053

Subgroups

	subgroup	G/H
center, Frattini	C₄	C₂×D₃×D₅
commutator, socle	C₂×C₃×C₅	C₂²×C₄
Fitting	C₂×C₃×C₄×C₅	C₂²
prime radical	#6817	C₂
cosocle	C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄	D₃×D₅
hypocenter	C₃×C₅	#131
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,4,5,3)(6,7,8)(11,17)(14,20)(18,23)(21,24);(7,8)(9,11,12,18,13,17,19,23)(10,14,15,21,16,20,22,24);(2,3)(4,5)(9,10,12,15,13,16,19,22)(11,14,18,21,17,20,23,24)

Polycyclic presentation:

2^5,3,5|a^2=d,b^2=d,d^2=e,g^a=g^4,c^b=ce,f^b=f^2

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746552, #11746553, #11747018, …
maximal normal subgroup of	#11746552, #11746553, #11747018, …
maximal quotient of	#11746851, #11746856, #11746860, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 366);