#455×Dic₅₃ #27389978

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

#455×Dic₅₃

Splittings

Sylow

C₅₃ ⋊ C₄×#455

Subgroups

	subgroup	G/H
center	C₂²	#120×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₂×C₅₃×#455	C₂
socle	C₂²×C₅₃	C₂×#120
prime radical	C₂×H(5,𝔽₂)×C₅₃	C₂²
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	C₂×#455	D₅₃
hypocenter	C₅₃	C₄×#455
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#455

1442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 3392

A minimal faithful permutation representation — 4 generators on 73 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);(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)(61,71)(64,69)(66,73)(67,70);(58,60)(59,63)(61,70)(62,68)(64,73)(65,72)(66,69)(67,71);(58,59,62,65)(60,66,68,73)(61,69,71,64)(63,70,72,67)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 175454);

#455×Dic53 #27389978