C₅×#64525 #13095059

order	1520
isoclinism	isoclinic class of #64525
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#64525

Splittings

Fitting	C₅×D₄×C₁₉ ⋊ C₂
Hall	C₅×C₁₉ ⋊ D₈
Sylow	C₁₉ ⋊ C₅×D₈

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂²⋊D₁₉
commutator, cosocle	C₄×C₁₉	C₂²×C₅
Frattini	C₄	C₂×C₅×D₁₉
Fitting	C₅×D₄×C₁₉	C₂
socle	C₂×C₅×C₁₉	D₄
hypercenter	C₅×D₄	D₁₉
hypocenter	C₁₉	C₅×D₈
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×D₄

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 760

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1520, 43);

C5×#64525 #13095059