C₂×D₉₄₉ #16838296

order	3796
automorphism	Aut(G) order 1639872
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₉₈
direct product	C₂×D₉₄₉
unambiguous semidirect product	(C₂×C₁₃)⋊D₇₃
unambiguous semidirect product	(C₂×C₇₃)⋊D₁₃

Splittings

Fitting, socle	C₂×C₁₃×C₇₃ ⋊ C₂
derived, Hall	C₁₃×C₇₃ ⋊ C₂²
Sylow	C₇₃ ⋊ C₂×D₁₃
Sylow	C₁₃ ⋊ C₂×D₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₄₉
commutator, cosocle, hypocenter	C₁₃×C₇₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₇₃	C₂
LCS	G ▷ C₁₃×C₇₃
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 88
transitive degree	μ_t(G) = 1898

A minimal faithful permutation representation — 2 generators on 88 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88);(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,88)(18,87)(19,86)(20,85)(21,84)(22,83)(23,82)(24,81)(25,80)(26,79)(27,78)(28,77)(29,76)(30,75)(31,74)(32,73)(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×#19151047, C₂×#19151048, C₂×(C₁₃⋊C₃)⋊D₇₃, …
maximal normal subgroup of	C₂×#19151047, C₂×#19151048, C₂×(C₁₃⋊C₃)⋊D₇₃, …
maximal quotient of	D₃×D₉₄₉, C₂×D₂₈₄₇, C₂×C₃×D₉₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3796, 13);

C2×D949 #16838296