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D₅×D₇×#120 #72218552

order	4480
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

D₅×D₇×#120

Splittings

Fitting	C₅×C₇×#120 ⋊ C₂²
Hall	C₅×C₇ ⋊ C₂²×#120
Sylow	C₇ ⋊ C₂×D₅×#120
Sylow	C₅ ⋊ C₂×D₇×#120

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₅×D₇
commutator, socle, cosocle	C₂²×C₅×C₇	C₂⁵
Fitting	C₅×C₇×#120	C₂²
hypercenter	#120	D₅×D₇
hypocenter	C₅×C₇	C₂²×#120
LCS	G ▷ C₂²×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂² ◁ #120

9088 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₅×#120×AGL(1,𝔽₇), D₇×AGL(1,𝔽₅)×#120
maximal normal subgroup of	D₅×#120×AGL(1,𝔽₇), D₇×AGL(1,𝔽₅)×#120

GAP

Past the SmallGroups library coverage — no SmallGroups id.