C₂×D₃₂₈₃ #27190069

order	13132
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₆₅₆₆
direct product	C₂×D₃₂₈₃
unambiguous semidirect product	(C₂×C₄₉)⋊D₆₇
unambiguous semidirect product	(C₂×C₆₇)⋊D₄₉

Splittings

Fitting	C₂×C₄₉×C₆₇ ⋊ C₂
derived, Hall	C₄₉×C₆₇ ⋊ C₂²
Sylow	C₆₇ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₃₂₈₃
commutator, cosocle, hypocenter	C₄₉×C₆₇	C₂²
Frattini	C₇	C₂×D₄₆₉
Fitting	C₂×C₄₉×C₆₇	C₂
socle	C₂×C₇×C₆₇	D₇
LCS	G ▷ C₄₉×C₆₇
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 118
transitive degree	μ_t(G) = 6566

A minimal faithful permutation representation — 2 generators on 118 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)(52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118);(4,51)(5,50)(6,49)(7,48)(8,47)(9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(53,118)(54,117)(55,116)(56,115)(57,114)(58,113)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,106)(66,105)(67,104)(68,103)(69,102)(70,101)(71,100)(72,99)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(85,86)

Conjugacy classes & character table

3286 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₃₁₃₂
maximal normal subgroup of	D₁₃₁₃₂
maximal quotient of	D₁₃₁₃₂, Dic₆₅₆₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13132, 9);

C2×D3283 #27190069