C₃×Dic₁₀₀ #11924823

order	1200
isoclinism	isoclinic class of Dic₁₀₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×Dic₁₀₀

Splittings

Hall	C₃×C₂₅ ⋊ Q₁₆
Sylow	C₂₅ ⋊ C₃×Q₁₆

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, prime radical	C₂×C₃×C₅	D₂₀
hypercenter	C₃×C₈	D₂₅
hypocenter	C₂₅	C₃×Q₁₆
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 1200

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3)(4,5,6,7,8,9,10,11)(12,19,18,17,16,15,14,13)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44);(4,12,8,16)(5,13,9,17)(6,14,10,18)(7,15,11,19)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)

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, 33);

C3×Dic100 #11924823