C₂×D₂₇₉ #11764355

order	1116
isoclinism	isoclinic class of D₂₇₉
automorphism	Aut(G) order 100440
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₅₅₈
direct product	C₂×D₂₇₉
unambiguous semidirect product	(C₂×C₉)⋊D₃₁
unambiguous semidirect product	(C₂×C₃₁)⋊D₉

Splittings

Fitting	C₂×C₉×C₃₁ ⋊ C₂
derived, Hall	C₉×C₃₁ ⋊ C₂²
Sylow	C₃₁ ⋊ C₂×D₉
Sylow	C₉ ⋊ C₂×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₂₇₉
commutator, cosocle, hypocenter	C₉×C₃₁	C₂²
Frattini	C₃	C₂×D₉₃
Fitting	C₂×C₉×C₃₁	C₂
socle	C₂×C₃×C₃₁	D₃
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 558

A minimal faithful permutation representation — 2 generators on 42 points:

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

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

Relationships

maximal subgroup of	D₁₁×D₂₇₉, C₂×C₁₁×D₂₇₉, C₂×D₃₀₆₉, …
maximal normal subgroup of	C₂×C₁₁×D₂₇₉, C₂×C₁₃×D₂₇₉, C₂×C₁₇×D₂₇₉, …
maximal quotient of	D₁₁×D₂₇₉, C₂×C₁₁×D₂₇₉, C₂×D₃₀₆₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1116, 14);

C2×D279 #11764355