Finite Group Databasebeta

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C₂×C₄×C₅×(C₃⋊D₃)⋊C₃ #72219474

order	2160
isoclinism	isoclinic class of (C₃⋊D₃)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄×C₅ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂×C₄×C₅×(C₃⋊D₃)⋊C₃

Splittings

Fitting	C₂×C₄×C₅×H(3,𝔽₃) ⋊ C₂
derived	C₃² ⋊ C₂²×C₃×C₄×C₅
Hall	C₅×H(3,𝔽₃) ⋊ C₂²×C₄
Sylow	H(3,𝔽₃) ⋊ C₂²×C₄×C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄×C₅	(C₃⋊D₃)⋊C₃
commutator, hypocenter	C₃²	C₂²×C₃×C₄×C₅
Frattini	C₂×C₃	C₂²×C₃×C₅×D₃
Fitting	C₂×C₄×C₅×H(3,𝔽₃)	C₂
socle	C₂²×C₃×C₅	C₂×C₃×D₃
prime radical	C₂²×C₅×(C₃⋊D₃)⋊C₃	C₂
cosocle	C₂×C₃²	C₂³×C₃×C₅
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄×C₅

410 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 156 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

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

Relationships

maximal subgroup of

C₂×C₄×C₅×PSU(3,𝔽₂)⋊C₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.