C₂×D₃₄₇₉ #28358153

order	13916
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₆₉₅₈
direct product	C₂×D₃₄₇₉
unambiguous semidirect product	(C₂×C₄₉)⋊D₇₁
unambiguous semidirect product	(C₂×C₇₁)⋊D₄₉

Splittings

Fitting	C₂×C₄₉×C₇₁ ⋊ C₂
derived, Hall	C₄₉×C₇₁ ⋊ C₂²
Sylow	C₇₁ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₃₄₇₉
commutator, cosocle, hypocenter	C₄₉×C₇₁	C₂²
Frattini	C₇	C₂×D₄₉₇
Fitting	C₂×C₄₉×C₇₁	C₂
socle	C₂×C₇×C₇₁	D₇
LCS	G ▷ C₄₉×C₇₁
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 122
transitive degree	μ_t(G) = 6958

A minimal faithful permutation representation — 2 generators on 122 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)(52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122);(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)(53,122)(54,121)(55,120)(56,119)(57,118)(58,117)(59,116)(60,115)(61,114)(62,113)(63,112)(64,111)(65,110)(66,109)(67,108)(68,107)(69,106)(70,105)(71,104)(72,103)(73,102)(74,101)(75,100)(76,99)(77,98)(78,97)(79,96)(80,95)(81,94)(82,93)(83,92)(84,91)(85,90)(86,89)(87,88)

Conjugacy classes & character table

3482 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₃₉₁₆
maximal normal subgroup of	D₁₃₉₁₆
maximal quotient of	D₁₃₉₁₆, Dic₆₉₅₈

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13916, 13);

C2×D3479 #28358153