C₄₃×#1044 #16864337

order	4300
isoclinism	isoclinic class of #1044
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₃ · Schur multiplier (H₂) = C₅

Aliases

direct product

C₄₃×#1044

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₄₃	#1044
commutator, hypocenter	C₅²	C₄×C₄₃
Frattini	C₁	G
Fitting, socle	C₅²×C₄₃	C₄
prime radical	C₄₃×C₅⋊D₅	C₂
cosocle	C₅⋊D₅	C₂×C₄₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄₃

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 430

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)(44,45)(46,49,47,51)(48,52,53,50);(45,51,53,48,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#1044×C₄₃⋊C₃, C₄₃×#64480, C₃×C₄₃×#1044, …
maximal normal subgroup of	#1044×C₄₃⋊C₃, C₃×C₄₃×#1044, #1044×C₄₃⋊C₇, …
maximal quotient of	C₃×C₄₃×#1044, C₄₃×C₃⋊#1044, C₇×C₄₃×#1044, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4300, 24);

C43×#1044 #16864337