C₆₁×Dic₅₃ #27188145

order	12932
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₆₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₆₁×Dic₅₃

Splittings

derived, Sylow	C₅₃ ⋊ C₄×C₆₁
Hall	C₅₃×C₆₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₆₁	D₅₃
commutator, hypocenter	C₅₃	C₄×C₆₁
Frattini	C₂	C₆₁×D₅₃
Fitting, socle, prime radical	C₂×C₅₃×C₆₁	C₂
cosocle	C₂×C₅₃	C₂×C₆₁
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂×C₆₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 118
transitive degree	μ_t(G) = 12932

A minimal faithful permutation representation — 2 generators on 118 points:

(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)(54,55,56,57)(58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

3416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12932, 2);

C61×Dic53 #27188145