C₂×D₇₃₅₃ #44440896

order	29412
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₄₇₀₆
direct product	C₂×D₇₃₅₃
unambiguous semidirect product	(C₂×C₉)⋊D₈₁₇
unambiguous semidirect product	(C₂×C₁₉)⋊D₃₈₇
unambiguous semidirect product	(C₂×C₄₃)⋊D₁₇₁

Splittings

Fitting	C₂×C₉×C₁₉×C₄₃ ⋊ C₂
derived, Hall	C₉×C₁₉×C₄₃ ⋊ C₂²
Hall	C₁₉×C₄₃ ⋊ C₂×D₉
Hall	C₉×C₄₃ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×D₄₃
Sylow	C₄₃ ⋊ C₂×D₁₇₁
Sylow	C₁₉ ⋊ C₂×D₃₈₇
Sylow	C₉ ⋊ C₂×D₈₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₇₃₅₃
commutator, cosocle, hypocenter	C₉×C₁₉×C₄₃	C₂²
Frattini	C₃	C₂×D₂₄₅₁
Fitting	C₂×C₉×C₁₉×C₄₃	C₂
socle	C₂×C₃×C₁₉×C₄₃	D₃
LCS	G ▷ C₉×C₁₉×C₄₃
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 14706

A minimal faithful permutation representation — 2 generators on 73 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);(4,11)(5,10)(6,9)(7,8)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(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

7356 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₉₄₁₂
maximal normal subgroup of	D₂₉₄₁₂
maximal quotient of	Dic₁₄₇₀₆, D₂₉₄₁₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29412, 58);

C2×D7353 #44440896