C₂×C₆₄×D₅₃ #27305125

order	13568
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₆₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₆₄×D₅₃

Splittings

Fitting	C₂×C₅₃×C₆₄ ⋊ C₂
derived, Sylow	C₅₃ ⋊ C₂²×C₆₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₆₄	D₅₃
commutator, hypocenter	C₅₃	C₂²×C₆₄
Frattini	C₃₂	C₂²×D₅₃
Fitting	C₂×C₅₃×C₆₄	C₂
socle	C₂²×C₅₃	C₂×C₃₂
prime radical	C₂²×D₅₃	C₃₂
cosocle	C₃₂×C₅₃	C₂³
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂×C₆₄

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 6784

A minimal faithful permutation representation — 3 generators on 119 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);(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)(56,57,58,63,59,64,68,78,60,65,69,79,72,82,88,98,61,66,70,80,73,83,89,99,75,85,91,101,94,104,108,113,62,67,71,81,74,84,90,100,76,86,92,102,95,105,109,114,77,87,93,103,96,106,110,115,97,107,111,116,112,117,118,119);(54,55)

Conjugacy classes & character table

3584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 90601);

C2×C64×D53 #27305125