C₂×D₄₉₃ #14520314

order	1972
isoclinism	isoclinic class of D₄₉₃
automorphism	Aut(G) order 441728
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₉₈₆
direct product	C₂×D₄₉₃
unambiguous semidirect product	(C₂×C₁₇)⋊D₂₉
unambiguous semidirect product	(C₂×C₂₉)⋊D₁₇

Splittings

Fitting, socle	C₂×C₁₇×C₂₉ ⋊ C₂
derived, Hall	C₁₇×C₂₉ ⋊ C₂²
Sylow	C₂₉ ⋊ C₂×D₁₇
Sylow	C₁₇ ⋊ C₂×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₉₃
commutator, cosocle, hypocenter	C₁₇×C₂₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₇×C₂₉	C₂
LCS	G ▷ C₁₇×C₂₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 986

A minimal faithful permutation representation — 2 generators on 48 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);(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(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

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

Relationships

maximal subgroup of	C₂×C₁₇⋊(D₂₉⋊C₇), D₇×D₄₉₃, C₂×D₃₄₅₁, …
maximal normal subgroup of	C₂×C₁₇⋊(D₂₉⋊C₇), C₂×C₇×D₄₉₃, C₂×C₁₁×D₄₉₃, …
maximal quotient of	D₇×D₄₉₃, C₂×D₃₄₅₁, C₂×C₇×D₄₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1972, 14);

C2×D493 #14520314