C₁₃×D₁₁₅ #15688463

order	2990
isoclinism	isoclinic class of D₁₁₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₁₁₅
unambiguous semidirect product	C₅⋊(C₁₃×D₂₃)
unambiguous semidirect product	C₂₃⋊(D₅×C₁₃)

Splittings

Fitting, socle, Hall	C₅×C₁₃×C₂₃ ⋊ C₂
derived, Hall	C₅×C₂₃ ⋊ C₂×C₁₃
Hall	C₁₃×C₂₃ ⋊ D₅
Hall	C₅×C₁₃ ⋊ D₂₃
Sylow	C₂₃ ⋊ D₅×C₁₃
Sylow	C₅ ⋊ C₁₃×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₁₁₅
commutator, cosocle, hypocenter	C₅×C₂₃	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₂₃	C₂
LCS	G ▷ C₅×C₂₃
UCS	C₁ ◁ C₁₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1495

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(15,18)(16,17)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₃×D₅₇₅, C₁₃×C₅⋊D₁₁₅, C₅×C₁₃×D₁₁₅, …
maximal normal subgroup of	C₅×C₁₃×D₁₁₅, C₇×C₁₃×D₁₁₅, C₁₁×C₁₃×D₁₁₅, …
maximal quotient of	C₁₃×D₅₇₅, C₁₃×C₅⋊D₁₁₅, C₅×C₁₃×D₁₁₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2990, 6);

C13×D115 #15688463