C₇×C₁₁⋊D₂₀₉ #44565687

order	32186
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₇×C₁₁⋊D₂₀₉
unambiguous semidirect product	C₁₁⋊(C₇×D₂₀₉)
unambiguous semidirect product	C₁₉⋊(C₇×C₁₁⋊D₁₁)

Splittings

Fitting, socle, Hall	C₇×C₁₁²×C₁₉ ⋊ C₂
derived, Hall	C₁₁²×C₁₉ ⋊ C₂×C₇
Hall	C₇×C₁₁² ⋊ D₁₉
Hall	C₇×C₁₉ ⋊ C₁₁⋊D₁₁
Sylow	C₁₁² ⋊ C₇×D₁₉
Sylow	C₁₉ ⋊ C₇×C₁₁⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₇	C₁₁⋊D₂₀₉
commutator, cosocle, hypocenter	C₁₁²×C₁₉	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₁²×C₁₉	C₂
LCS	G ▷ C₁₁²×C₁₉
UCS	C₁ ◁ C₇

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 16093

A minimal faithful permutation representation — 3 generators on 48 points:

(1,2,3,4,5,6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(20,21)(22,23)(24,25)(26,27)(28,29)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48);(19,20,22,24,26,28,29,27,25,23,21)(30,31,33,35,37,39,41,43,45,47,48,46,44,42,40,38,36,34,32);(8,9,11,13,15,17,18,16,14,12,10)

Conjugacy classes & character table

8057 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32186, 14);

C7×C11⋊D209 #44565687