Finite Group Databasebeta

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D₅×#12364 #72221521

order	2560
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₅×#12364 ⋊ C₂
Sylow	C₅ ⋊ C₂×#12364

Subgroups

	subgroup	G/H
center	C₂	D₅×#1629
commutator, cosocle	C₄×C₅×C₈	C₂⁴
Frattini	C₄×C₈	C₂³×D₅
Fitting	C₅×#12364	C₂
socle	C₂×C₅	C₂×#1629
prime radical	D₅×#3291	C₂
hypercenter	#12364	D₅
hypocenter	C₅	C₂×#12364
LCS	G ▷ C₄×C₅×C₈ ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #12364

1926 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×#12364
maximal normal subgroup of	AGL(1,𝔽₅)×#12364

GAP

Past the SmallGroups library coverage — no SmallGroups id.