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C₂×C₃×(#1043⋊C₅)⋊C₂ #72219009

order	6000
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₃×(#1043⋊C₅)⋊C₂

Splittings

Fitting	C₂×C₃×H(3,𝔽₅) ⋊ C₂×C₄
derived, Sylow	H(3,𝔽₅) ⋊ C₂²×C₃×C₄
Hall	C₃×H(3,𝔽₅) ⋊ C₂²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(#1043⋊C₅)⋊C₂
commutator, hypocenter	H(3,𝔽₅)	C₂²×C₃×C₄
Frattini	C₅	C₂×C₃×D₅×AGL(1,𝔽₅)
Fitting	C₂×C₃×H(3,𝔽₅)	C₂×C₄
socle	C₂×C₃×C₅	D₅×AGL(1,𝔽₅)
prime radical	C₂×C₃×((C₅⋊D₅)⋊C₅)⋊C₂	C₂
cosocle	(C₅⋊D₅)⋊C₅	C₂³×C₃
LCS	G ▷ H(3,𝔽₅)
UCS	C₁ ◁ C₂×C₃

398 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃×#14522510
maximal normal subgroup of	C₂×C₃×#14522510

GAP

Past the SmallGroups library coverage — no SmallGroups id.