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C₁₉×#1043 #14273995

order	1900
isoclinism	isoclinic class of #1043
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting, socle, Hall	C₅²×C₁₉ ⋊ C₄
derived, Sylow	C₅² ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	#1043
commutator, hypocenter	C₅²	C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₉	C₄
prime radical	C₁₉×C₅⋊D₅	C₂
cosocle	C₅⋊D₅	C₂×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 475

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×C₁₉×#1043, C₁₉×C₇⋊#1043, C₁₉×#11744707, …
maximal normal subgroup of	C₇×C₁₉×#1043, C₁₁×C₁₉×#1043, C₁₃×C₁₉×#1043, …
maximal quotient of	C₇×C₁₉×#1043, C₁₉×C₇⋊#1043, C₁₉×#11744707, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1900, 20);