D₅₃×#1374 #27298927

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₆ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

D₅₃×#1374

Splittings

Fitting	C₅₃×#1374 ⋊ C₂
Sylow	C₅₃ ⋊ C₂×#1374

Subgroups

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₅₃
commutator	C₂×C₅₃	C₂×C₄×C₁₆
Fitting	C₅₃×#1374	C₂
socle	C₂³×C₅₃	C₂²×C₈
prime radical	C₂³×D₅₃	C₂×C₈
cosocle	C₂²×C₈×C₅₃	C₂³
hypercenter	#1374	D₅₃
hypocenter	C₅₃	C₂×#1374
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₈ ◁ #1374

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 6784

A minimal faithful permutation representation — 3 generators on 77 points:

(1,2,3,4)(6,8)(25,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27);(5,6)(7,8)(9,10,11,14,12,15,17,20,13,16,18,21,19,22,23,24);(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)

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 84403);

D53×#1374 #27298927