C₅×Dic₇₉ #13096818

order	1580
isoclinism	isoclinic class of D₇₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×Dic₇₉
unambiguous semidirect product	C₇₉⋊(C₄×C₅)

Splittings

derived, Sylow	C₇₉ ⋊ C₄×C₅
Hall	C₅×C₇₉ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₇₉
commutator, hypocenter	C₇₉	C₄×C₅
Frattini	C₂	C₅×D₇₉
Fitting, socle, prime radical	C₂×C₅×C₇₉	C₂
cosocle	C₂×C₇₉	C₂×C₅
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂×C₅

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 88
transitive degree	μ_t(G) = 1580

A minimal faithful permutation representation — 2 generators on 88 points:

(1,2,3,4,5)(6,7)(8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88);(6,8,7,9)(11,88)(12,87)(13,86)(14,85)(15,84)(16,83)(17,82)(18,81)(19,80)(20,79)(21,78)(22,77)(23,76)(24,75)(25,74)(26,73)(27,72)(28,71)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₅×Dic₇₉, C₅×Dic₂₃₇, C₅×(C₇₉⋊C₃)⋊C₄, …
maximal normal subgroup of	C₃×C₅×Dic₇₉, C₅×(C₇₉⋊C₃)⋊C₄, C₅×C₇×Dic₇₉, …
maximal quotient of	C₃×C₅×Dic₇₉, C₅×Dic₂₃₇, C₅×C₇×Dic₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1580, 2);

C5×Dic79 #13096818