C₂×D₃₃₃₇ #27211153

order	13348
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₆₆₇₄
direct product	C₂×D₃₃₃₇
unambiguous semidirect product	(C₂×C₄₇)⋊D₇₁
unambiguous semidirect product	(C₂×C₇₁)⋊D₄₇

Splittings

Fitting, socle	C₂×C₄₇×C₇₁ ⋊ C₂
derived, Hall	C₄₇×C₇₁ ⋊ C₂²
Sylow	C₇₁ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×D₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₃₃₃₇
commutator, cosocle, hypocenter	C₄₇×C₇₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₄₇×C₇₁	C₂
LCS	G ▷ C₄₇×C₇₁
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 120
transitive degree	μ_t(G) = 6674

A minimal faithful permutation representation — 2 generators on 120 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);(4,49)(5,48)(6,47)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(51,120)(52,119)(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

3340 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₃₃₄₈
maximal normal subgroup of	D₁₃₃₄₈
maximal quotient of	D₁₃₃₄₈, Dic₆₆₇₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13348, 7);

C2×D3337 #27211153