C₂₅×Dic₁₂ #11924843

order	1200
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₅ · Schur multiplier (H₂) = C₁

metacyclic
supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₂₅×Dic₁₂

Splittings

Hall	C₃×C₂₅ ⋊ Q₁₆
Sylow	C₃ ⋊ Q₁₆×C₂₅

Subgroups

	subgroup	G/H
center	C₂×C₂₅	D₁₂
commutator	C₃×C₄	C₂²×C₂₅
Frattini	C₄×C₅	C₂×C₅×D₃
Fitting	C₃×C₈×C₂₅	C₂
socle, prime radical	C₂×C₃×C₅	C₅×D₄
cosocle	C₃×C₄×C₅	C₂²×C₅
hypercenter	C₈×C₂₅	D₃
hypocenter	C₃	Q₁₆×C₂₅
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₂₅ ◁ C₄×C₂₅ ◁ C₈×C₂₅

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 53);

C25×Dic12 #11924843