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C₃×C₇²×Dic₃×C₁₉ #45691970

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₇²×C₁₉ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₃×C₇²×Dic₃×C₁₉
unambiguous semidirect product	C₃⋊(C₃×C₄×C₇²×C₁₉)

Splittings

derived	C₃ ⋊ C₃×C₄×C₇²×C₁₉
Hall	C₃²×C₇²×C₁₉ ⋊ C₄
Hall	C₃²×C₇² ⋊ C₄×C₁₉
Hall	C₃²×C₁₉ ⋊ C₄×C₇²
Sylow	C₃² ⋊ C₄×C₇²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇²×C₁₉	D₃
commutator, hypocenter	C₃	C₃×C₄×C₇²×C₁₉
Frattini	C₂	C₃×D₃×C₇²×C₁₉
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₉	C₂
cosocle	C₂×C₃	C₂×C₃×C₇²×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₇²×C₁₉

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11172

Conjugacy classes & character table

16758 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 768);