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D₃×(C₂²⋊C₉)⋊C₄ #11722265

order	864
isoclinism	isoclinic class of D₃×(C₂²⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₃×(C₂²⋊C₉)⋊C₄
unambiguous semidirect product	(D₃×C₂²⋊C₉)⋊C₄

Splittings

C₃×C₂²⋊C₉ ⋊ C₂×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₃×(C₂²⋊C₉)⋊C₂
commutator, hypocenter	C₃×C₂²⋊C₉	C₂×C₄
Frattini	C₂×C₃	D₃×S₄
Fitting, socle	C₂³×C₃²	C₂×D₃
prime radical	C₂³×C₃×D₃	D₃
cosocle	C₂×C₃×C₂²⋊C₉	C₂²
LCS	G ▷ C₃×C₂²⋊C₉
UCS	C₁ ◁ C₂

239 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 239 conjugacy classes of subgroups — too many to draw. Only its 39 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) = 72

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×(C₂²⋊C₉)⋊Q₈, #13164159, #13164160, …
maximal normal subgroup of	D₃×(C₂²⋊C₉)⋊Q₈, #13164159, #13164160, …
maximal quotient of	D₃×(C₂²⋊C₉)⋊C₈, #13146272, #13146299, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 2232);