C₂×D₇₁₃₇ #43269708

order	28548
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₄₂₇₄
direct product	C₂×D₇₁₃₇
unambiguous semidirect product	(C₂×C₉)⋊D₇₉₃
unambiguous semidirect product	(C₂×C₁₃)⋊D₅₄₉
unambiguous semidirect product	(C₂×C₆₁)⋊D₁₁₇

Splittings

Fitting	C₂×C₉×C₁₃×C₆₁ ⋊ C₂
derived, Hall	C₉×C₁₃×C₆₁ ⋊ C₂²
Hall	C₁₃×C₆₁ ⋊ C₂×D₉
Hall	C₉×C₆₁ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₆₁
Sylow	C₆₁ ⋊ C₂×D₁₁₇
Sylow	C₁₃ ⋊ C₂×D₅₄₉
Sylow	C₉ ⋊ C₂×D₇₉₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₇₁₃₇
commutator, cosocle, hypocenter	C₉×C₁₃×C₆₁	C₂²
Frattini	C₃	C₂×D₂₃₇₉
Fitting	C₂×C₉×C₁₃×C₆₁	C₂
socle	C₂×C₃×C₁₃×C₆₁	D₃
LCS	G ▷ C₉×C₁₃×C₆₁
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 85
transitive degree	μ_t(G) = 14274

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

Conjugacy classes & character table

7140 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₈₅₄₈
maximal normal subgroup of	D₂₈₅₄₈
maximal quotient of	Dic₁₄₂₇₄, D₂₈₅₄₈

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28548, 94);

C2×D7137 #43269708