C₃×#87802 #11925195

order	1200
isoclinism	isoclinic class of #87800
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₅

Aliases

direct product

C₃×#87802

Splittings

Hall	C₃×C₅² ⋊ Q₁₆
Sylow	C₅² ⋊ C₃×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₃	C₄⋊(C₅⋊D₅)
commutator, cosocle	C₄×C₅²	C₂²×C₃
Frattini	C₄	C₂×C₃×C₅⋊D₅
Fitting	C₃×C₅²×C₈	C₂
socle, prime radical	C₂×C₃×C₅²	D₄
hypercenter	C₃×C₈	C₅⋊D₅
hypocenter	C₅²	C₃×Q₁₆
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1200

A minimal faithful permutation representation — 3 generators on 29 points:

(1,2,3)(4,6,13,17,8,15,7,14)(5,9,16,19,11,18,10,12)(25,26,28,29,27);(4,5,8,11)(6,12,15,19)(7,16,13,10)(9,17,18,14)(21,22)(23,24)(26,27)(28,29);(20,21,23,24,22)

Conjugacy classes & character table

309 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 405);

C3×#87802 #11925195