C₇×D₁₄₅ #14523202

order	2030
isoclinism	isoclinic class of D₁₄₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₁₄₅
unambiguous semidirect product	C₅⋊(C₇×D₂₉)

Splittings

Fitting, socle, Hall	C₅×C₇×C₂₉ ⋊ C₂
derived, Hall	C₅×C₂₉ ⋊ C₂×C₇
Hall	C₇×C₂₉ ⋊ D₅
Hall	C₅×C₇ ⋊ D₂₉
Sylow	C₂₉ ⋊ C₇×D₅
Sylow	C₅ ⋊ C₇×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₁₄₅
commutator, cosocle, hypocenter	C₅×C₂₉	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₂₉	C₂
LCS	G ▷ C₅×C₂₉
UCS	C₁ ◁ C₇

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1015

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×#10596814, C₇×#10596815, C₇⋊#10596814, …
maximal normal subgroup of	C₇×#10596814, C₇×#10596815, C₇⋊#10596814, …
maximal quotient of	C₇×Dic₁₄₅, C₂×C₇×D₁₄₅, C₄₉×D₁₄₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2030, 7);

C7×D145 #14523202