C₅₃×#595 #16813356

order	3604
isoclinism	isoclinic class of #595
automorphism	?
homology	Abelianization (H₁) = C₄×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅₃×#595

Splittings

Fitting, socle, Hall	C₁₇×C₅₃ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₄×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅₃	#595
commutator, hypocenter	C₁₇	C₄×C₅₃
Frattini	C₁	G
Fitting, socle	C₁₇×C₅₃	C₄
prime radical	D₁₇×C₅₃	C₂
cosocle	D₁₇	C₂×C₅₃
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₅₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 901

A minimal faithful permutation representation — 2 generators on 70 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)(55,56,57,59)(58,61,62,66)(60,65,63,64)(67,69,70,68);(54,55,58,63,59,64,68,70,66,61,67,69,65,56,60,62,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₅₃×#595, C₅₃×C₃⋊#595, C₅×C₅₃×#595, …
maximal normal subgroup of	C₃×C₅₃×#595, C₅×C₅₃×#595, C₇×C₅₃×#595
maximal quotient of	C₃×C₅₃×#595, C₅₃×C₃⋊#595, C₅×C₅₃×#595, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3604, 7);

C53×#595 #16813356