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C₃×(C₁₉⋊C₃)⋊(C₇⋊Dic₇) #45691882

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃×C₇

Aliases

direct product	C₃×(C₁₉⋊C₃)⋊(C₇⋊Dic₇)
unambiguous semidirect product	(C₁₉⋊C₃)⋊(C₃×C₇⋊Dic₇)

Splittings

derived, Hall	C₇²×C₁₉ ⋊ C₃²×C₄
Hall	C₃×C₇²×C₁₉⋊C₃ ⋊ C₄
Hall	C₇⋊Dic₁₃₃ ⋊ C₃²
Hall	C₃×C₁₉⋊C₃ ⋊ C₇⋊Dic₇
Sylow	C₇² ⋊ C₃×(C₁₉⋊C₃)⋊C₄
Sylow	C₁₉ ⋊ C₃²×C₇⋊Dic₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₁₉⋊C₃)⋊(C₇⋊D₇)
commutator, hypocenter	C₇²×C₁₉	C₃²×C₄
Frattini	C₂	C₃×(C₁₉⋊C₃)⋊(C₇⋊D₇)
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₇²×C₁₉⋊C₃	C₂
cosocle	C₂×C₇²×C₁₉	C₂×C₃²
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11172

Conjugacy classes & character table

1350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 680);