C₁₇×D₅₃ #14268558

order	1802
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₅₃
unambiguous semidirect product	C₅₃⋊(C₂×C₁₇)

Splittings

Fitting, socle, Hall	C₁₇×C₅₃ ⋊ C₂
derived, Sylow	C₅₃ ⋊ C₂×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₅₃
commutator, cosocle, hypocenter	C₅₃	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₅₃	C₂
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₁₇

8 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)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70);(19,70)(20,69)(21,68)(22,67)(23,66)(24,65)(25,64)(26,63)(27,62)(28,61)(29,60)(30,59)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₇×#6157, #16813360, D₁₇×D₅₃, …
maximal normal subgroup of	C₁₇×#6157, #16813360, D₁₇×D₅₃, …
maximal quotient of	C₁₇×Dic₅₃, C₂×C₁₇×D₅₃, C₇×C₁₇×D₅₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1802, 2);

C17×D53 #14268558