C₃×#87713 #11924826

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

Aliases

direct product

C₃×#87713

Splittings

Fitting	C₃×C₈×C₂₅ ⋊ C₂
Hall	C₃×C₂₅ ⋊ SD₁₆
Sylow	C₂₅ ⋊ C₃×SD₁₆

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
prime radical	C₃×D₁₀₀	C₂
hypercenter	C₃×C₈	D₂₅
hypocenter	C₂₅	C₃×SD₁₆
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

60 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)(4,17,25,13,20,10,9,28,14,12,19,5,22,27,7,11,18,15,26,16,6,24,8,21,23)(29,30,31,33,32,34,35,36);(5,7)(6,10)(8,13)(9,16)(11,19)(12,18)(14,15)(17,23)(20,24)(21,25)(22,27)(26,28)(30,33)(31,35)(34,36)

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, 36);

C3×#87713 #11924826