C₄₃×#1042 #16864339

order	4300
isoclinism	isoclinic class of #1042
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₄₃×#1042

Splittings

Fitting, socle, Hall	C₅²×C₄₃ ⋊ C₄
derived, Sylow	C₅² ⋊ C₄×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄₃	#1042
commutator, hypocenter	C₅²	C₄×C₄₃
Frattini	C₁	G
Fitting, socle	C₅²×C₄₃	C₄
prime radical	C₅×D₅×C₄₃	C₂
cosocle	C₅×D₅	C₂×C₄₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄₃

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 860

A minimal faithful permutation representation — 2 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43)(45,46)(47,48)(50,51,52,53);(44,45,47,48,46)(49,50,53,51,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#1042×C₄₃⋊C₃, C₃×C₄₃×#1042, C₄₃×C₃⋊#1042, …
maximal normal subgroup of	#1042×C₄₃⋊C₃, C₃×C₄₃×#1042, #1042×C₄₃⋊C₇, …
maximal quotient of	C₃×C₄₃×#1042, C₄₃×C₃⋊#1042, C₇×C₄₃×#1042, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4300, 26);

C43×#1042 #16864339