C₂×C₁₉×C₇₁⋊C₅ #27212549

order	13490
isoclinism	isoclinic class of C₇₁⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₉×C₇₁⋊C₅
unambiguous semidirect product	(C₂×C₇₁)⋊(C₅×C₁₉)
unambiguous semidirect product	(C₂×C₁₉×C₇₁)⋊C₅

Splittings

Fitting, socle, Hall	C₂×C₁₉×C₇₁ ⋊ C₅
derived, Sylow	C₇₁ ⋊ C₂×C₅×C₁₉
Hall	C₁₉×C₇₁ ⋊ C₂×C₅
Hall	C₂×C₇₁ ⋊ C₅×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₇₁⋊C₅
commutator, cosocle, hypocenter	C₇₁	C₂×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₇₁	C₅
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₂×C₁₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 92
transitive degree	μ_t(G) = 2698

A minimal faithful permutation representation — 2 generators on 92 points:

(2,3,5,9,17)(4,7,13,24,39)(6,11,21,25,30)(8,15,28,45,16)(10,19,32,18,31)(12,23,38,57,58)(14,26,42,60,49)(20,34,53,40,59)(22,36,46,41,50)(27,44,63,48,67)(29,47,65,37,56)(33,52,35,43,51)(54,70,61,71,68)(55,66,64,62,69)(72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90)(91,92);(1,2,4,8,16,5,10,20,31,50,13,25,41,52,69,28,46,64,70,71,15,29,48,34,54,17,30,49,56,45,32,51,68,59,65,53,60,7,14,27,19,33,23,24,40,36,55,44,42,61,39,58,67,63,3,6,12,9,18,11,22,37,21,35,26,43,62,38,57,47,66)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄×C₁₉×C₇₁⋊C₅, C₁₉×Dic₇₁⋊C₅, Dic₁₉×C₇₁⋊C₅, …
maximal normal subgroup of	C₄×C₁₉×C₇₁⋊C₅, C₁₉×Dic₇₁⋊C₅, Dic₁₉×C₇₁⋊C₅, …
maximal quotient of	C₄×C₁₉×C₇₁⋊C₅, C₂²×C₁₉×C₇₁⋊C₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13490, 2);

C2×C19×C71⋊C5 #27212549