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#91529

order	480
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

Splittings

Hall	C₃×C₅ ⋊ #117
Sylow	C₅ ⋊ #877
Sylow	C₃ ⋊ #4072

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄
Fitting, prime radical	C₂³×C₃×C₅	C₂²
socle, cosocle	C₂²×C₃×C₅	C₂³
hypercenter	C₂³	D₃×D₅
hypocenter	C₃×C₅	#117
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂³

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 20 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11747130, #11749173, #11752780, …
maximal normal subgroup of	#11747130, #11749173, #11752780, …
maximal quotient of	#11748329, #11748330, #11748337, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 605);