C₁₃×D₇₅ #14519600

order	1950
isoclinism	isoclinic class of D₇₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₇₅
unambiguous semidirect product	C₃⋊(C₁₃×D₂₅)
unambiguous semidirect product	C₂₅⋊(D₃×C₁₃)

Splittings

Fitting, Hall	C₃×C₁₃×C₂₅ ⋊ C₂
derived, Hall	C₃×C₂₅ ⋊ C₂×C₁₃
Hall	C₁₃×C₂₅ ⋊ D₃
Hall	C₃×C₁₃ ⋊ D₂₅
Sylow	C₂₅ ⋊ D₃×C₁₃
Sylow	C₃ ⋊ C₁₃×D₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₇₅
commutator, cosocle, hypocenter	C₃×C₂₅	C₂×C₁₃
Frattini	C₅	C₁₃×D₁₅
Fitting	C₃×C₁₃×C₂₅	C₂
socle	C₃×C₅×C₁₃	D₅
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 975

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);(15,16)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₃×D₇₅, D₃×C₁₃×D₂₅, D₃₉⋊D₂₅, …
maximal normal subgroup of	D₁₃×D₇₅, D₃×C₁₃×D₂₅, D₃₉⋊D₂₅, …
maximal quotient of	C₁₃×Dic₇₅, C₂×C₁₃×D₇₅, C₇×C₁₃×D₇₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 10);

C13×D75 #14519600