C₂×D₄₈₁ #14515327

order	1924
isoclinism	isoclinic class of D₄₈₁
automorphism	Aut(G) order 415584
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₉₆₂
direct product	C₂×D₄₈₁
unambiguous semidirect product	(C₂×C₁₃)⋊D₃₇
unambiguous semidirect product	(C₂×C₃₇)⋊D₁₃

Splittings

Fitting, socle	C₂×C₁₃×C₃₇ ⋊ C₂
derived, Hall	C₁₃×C₃₇ ⋊ C₂²
Sylow	C₃₇ ⋊ C₂×D₁₃
Sylow	C₁₃ ⋊ C₂×D₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₈₁
commutator, cosocle, hypocenter	C₁₃×C₃₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₃₇	C₂
LCS	G ▷ C₁₃×C₃₇
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 962

A minimal faithful permutation representation — 2 generators on 52 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52);(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,52)(18,51)(19,50)(20,49)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₇×D₄₈₁, C₂×D₃₃₆₇, C₂×C₇×D₄₈₁, …
maximal normal subgroup of	C₂×C₇×D₄₈₁, C₂×C₁₁×D₄₈₁, C₂×C₁₃×D₄₈₁, …
maximal quotient of	D₇×D₄₈₁, C₂×D₃₃₆₇, C₂×C₇×D₄₈₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1924, 14);

C2×D481 #14515327