C₇×Dic₇₁ #14521900

order	1988
isoclinism	isoclinic class of D₇₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇×Dic₇₁

Splittings

derived, Sylow	C₇₁ ⋊ C₄×C₇
Hall	C₇×C₇₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇	D₇₁
commutator, hypocenter	C₇₁	C₄×C₇
Frattini	C₂	C₇×D₇₁
Fitting, socle, prime radical	C₂×C₇×C₇₁	C₂
cosocle	C₂×C₇₁	C₂×C₇
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₂×C₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 82
transitive degree	μ_t(G) = 1988

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	Dic₇₁⋊C₄₉, C₄₉×Dic₇₁, C₇×Dic₇₁⋊C₇, …
maximal normal subgroup of	Dic₇₁⋊C₄₉, C₄₉×Dic₇₁, C₇×Dic₇₁⋊C₇, …
maximal quotient of	C₄₉×Dic₇₁, C₇²×Dic₇₁, C₇×Dic₄₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1988, 4);

C7×Dic71 #14521900