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C₉×C₅₃×Dic₁₉ #49136205

order	36252
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₅₃×Dic₁₉

Splittings

derived, Sylow	C₁₉ ⋊ C₄×C₉×C₅₃
Hall	C₉×C₁₉×C₅₃ ⋊ C₄
Hall	C₁₉×C₅₃ ⋊ C₄×C₉
Hall	C₉×C₁₉ ⋊ C₄×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₅₃	D₁₉
commutator, hypocenter	C₁₉	C₄×C₉×C₅₃
Frattini	C₂×C₃	C₃×D₁₉×C₅₃
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle, prime radical	C₂×C₃×C₁₉×C₅₃	C₂×C₃
cosocle	C₂×C₃×C₁₉	C₂×C₃×C₅₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₉×C₅₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 36252

Conjugacy classes & character table

10494 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 4);