C₇×Dic₇₃ #14523285

order	2044
isoclinism	isoclinic class of D₇₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇×Dic₇₃

Splittings

derived, Sylow	C₇₃ ⋊ C₄×C₇
Hall	C₇×C₇₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇	D₇₃
commutator, hypocenter	C₇₃	C₄×C₇
Frattini	C₂	C₇×D₇₃
Fitting, socle, prime radical	C₂×C₇×C₇₃	C₂
cosocle	C₂×C₇₃	C₂×C₇
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 84
transitive degree	μ_t(G) = 2044

A minimal faithful permutation representation — 2 generators on 84 points:

(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84);(8,10,9,11)(13,84)(14,83)(15,82)(16,81)(17,80)(18,79)(19,78)(20,77)(21,76)(22,75)(23,74)(24,73)(25,72)(26,71)(27,70)(28,69)(29,68)(30,67)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,59)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₉×Dic₇₃, C₇²×Dic₇₃, C₇×Dic₅₁₁, …
maximal normal subgroup of	C₄₉×Dic₇₃, C₇²×Dic₇₃, C₇×C₁₁×Dic₇₃, …
maximal quotient of	C₄₉×Dic₇₃, C₇²×Dic₇₃, C₇×Dic₅₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2044, 3);

C7×Dic73 #14523285