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C₃×#87830 #11925316

order	1200
isoclinism	isoclinic class of D₅⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₄

Aliases

Splittings

derived, Sylow	C₅² ⋊ C₃×C₄²
Hall	C₃×C₅² ⋊ C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₅⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅²	C₃×C₄²
Frattini	C₂	C₃×D₅⋊AGL(1,𝔽₅)
Fitting, socle	C₂×C₃×C₅²	C₂×C₄
prime radical	C₂×C₃×C₅⋊D₅	C₂²
cosocle	C₂×C₅⋊D₅	C₂²×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 17 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#87830, C₃×#11717375, #72224578, …
maximal normal subgroup of	D₃×#87830, C₃×#11717375, #72224578, …
maximal quotient of	C₃×#11925354, C₃²×#87830, C₃×#11716761, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 526);