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C₁₁²×Dic₃×C₁₉ #42119965

order	27588
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁²×C₁₉ · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₁₁²×Dic₃×C₁₉
unambiguous semidirect product	C₃⋊(C₄×C₁₁²×C₁₉)

Splittings

derived, Sylow	C₃ ⋊ C₄×C₁₁²×C₁₉
Hall	C₃×C₁₁²×C₁₉ ⋊ C₄
Hall	C₃×C₁₁² ⋊ C₄×C₁₉
Hall	C₃×C₁₉ ⋊ C₄×C₁₁²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁²×C₁₉	D₃
commutator, hypocenter	C₃	C₄×C₁₁²×C₁₉
Frattini	C₂	D₃×C₁₁²×C₁₉
Fitting, socle, prime radical	C₂×C₃×C₁₁²×C₁₉	C₂
cosocle	C₂×C₃	C₂×C₁₁²×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₁²×C₁₉

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 27588

Conjugacy classes & character table

13794 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 57);