C₃×D₂₀₀ #11924827

order	1200
isoclinism	isoclinic class of Dic₁₀₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×D₂₀₀

Splittings

Fitting	C₃×C₈×C₂₅ ⋊ C₂
Hall	C₃×C₂₅ ⋊ D₈
Sylow	C₂₅ ⋊ C₃×D₈

Subgroups

	subgroup	G/H
center	C₂×C₃	D₁₀₀
commutator, cosocle	C₄×C₂₅	C₂²×C₃
Frattini	C₄×C₅	C₂×C₃×D₅
Fitting	C₃×C₈×C₂₅	C₂
socle	C₂×C₃×C₅	D₂₀
hypercenter	C₃×C₈	D₂₅
hypocenter	C₂₅	C₃×D₈
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 600

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3)(4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36);(5,11)(6,10)(7,9)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

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, 37);

C3×D200 #11924827