C₂×D₂₈₇ #11765976

order	1148
isoclinism	isoclinic class of D₂₈₇
automorphism	Aut(G) order 137760
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₅₇₄
direct product	C₂×D₂₈₇
unambiguous semidirect product	(C₂×C₇)⋊D₄₁
unambiguous semidirect product	(C₂×C₄₁)⋊D₇

Splittings

Fitting, socle	C₂×C₇×C₄₁ ⋊ C₂
derived, Hall	C₇×C₄₁ ⋊ C₂²
Sylow	C₄₁ ⋊ C₂×D₇
Sylow	C₇ ⋊ C₂×D₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₂₈₇
commutator, cosocle, hypocenter	C₇×C₄₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₄₁	C₂
LCS	G ▷ C₇×C₄₁
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 574

A minimal faithful permutation representation — 2 generators on 50 points:

(1,2)(3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(4,9)(5,8)(6,7)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(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

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

Relationships

maximal subgroup of	C₂×ΓL(1,𝔽₈)⋊D₄₁, D₃×D₂₈₇, C₂×C₃×D₂₈₇, …
maximal normal subgroup of	C₂×ΓL(1,𝔽₈)⋊D₄₁, C₂×C₃×D₂₈₇, C₂×C₁₁×D₂₈₇, …
maximal quotient of	D₃×D₂₈₇, C₂×C₃×D₂₈₇, C₂×D₈₆₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1148, 10);

C2×D287 #11765976