C₅×Dic₇₆ #13095052

order	1520
isoclinism	isoclinic class of #64516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×Dic₇₆

Splittings

Hall	C₅×C₁₉ ⋊ Q₁₆
Sylow	C₁₉ ⋊ C₅×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₅	D₇₆
commutator, cosocle	C₄×C₁₉	C₂²×C₅
Frattini	C₄	C₂×C₅×D₁₉
Fitting	C₅×C₈×C₁₉	C₂
socle, prime radical	C₂×C₅×C₁₉	D₄
hypercenter	C₅×C₈	D₁₉
hypocenter	C₁₉	C₅×Q₁₆
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 1520

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13)(14,21,20,19,18,17,16,15)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40);(6,14,10,18)(7,15,11,19)(8,16,12,20)(9,17,13,21)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1520, 36);

C5×Dic76 #13095052