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C₃×C₁₉×Dic₇ #13097595

order	1596
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₁₉×Dic₇

Splittings

derived, Sylow	C₇ ⋊ C₃×C₄×C₁₉
Hall	C₃×C₇×C₁₉ ⋊ C₄
Hall	C₇×C₁₉ ⋊ C₃×C₄
Hall	C₃×C₇ ⋊ C₄×C₁₉

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1596

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24)(25,26)(27,28,29,30,31,32,33);(23,25,24,26)(28,33)(29,32)(30,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	Dic₇×#4294, C₁₉×Dic₇⋊C₉, #18012094, …
maximal normal subgroup of	Dic₇×#4294, C₁₉×Dic₇⋊C₉, #18012094, …
maximal quotient of	C₉×C₁₉×Dic₇, C₃²×C₁₉×Dic₇, C₃×C₁₉×Dic₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1596, 18);