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D₃×#10620710 #72244265

order	4032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

D₃×#10620710

Splittings

Fitting	C₃×C₄²×C₇ ⋊ C₂²×C₃
Hall	C₃×ΓL(1,𝔽₈) ⋊ C₂×#127
Sylow	C₇ ⋊ C₃×D₃×#127

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₃×C₇	C₂⁴×C₃
Fitting	C₃×C₄²×C₇	C₂²×C₃
hypercenter	C₄²	D₃×AGL(1,𝔽₇)
hypocenter	C₃×C₇	C₂×C₃×#127
LCS	G ▷ C₂²×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂² ◁ C₄²

2100 conjugacy classes of subgroups; only the 331 normal subgroups are shown.

normal subgroups only

This group has 2100 conjugacy classes of subgroups — too many to draw. Only its 331 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 336

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#127×AGL(1,𝔽₇), C₃⋊D₃×#10620710, D₃×#89594⋊C₃
maximal normal subgroup of	D₃×#127×AGL(1,𝔽₇), D₃×#89594⋊C₃
maximal quotient of	C₃⋊D₃×#10620710

GAP

Past the SmallGroups library coverage — no SmallGroups id.