C₂×D₃₇₁₃ #28415360

order	14852
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₇₄₂₆
direct product	C₂×D₃₇₁₃
unambiguous semidirect product	(C₂×C₄₇)⋊D₇₉
unambiguous semidirect product	(C₂×C₇₉)⋊D₄₇

Splittings

Fitting, socle	C₂×C₄₇×C₇₉ ⋊ C₂
derived, Hall	C₄₇×C₇₉ ⋊ C₂²
Sylow	C₇₉ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×D₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₃₇₁₃
commutator, cosocle, hypocenter	C₄₇×C₇₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₄₇×C₇₉	C₂
LCS	G ▷ C₄₇×C₇₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 128
transitive degree	μ_t(G) = 7426

A minimal faithful permutation representation — 2 generators on 128 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)(50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128);(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)(51,128)(52,127)(53,126)(54,125)(55,124)(56,123)(57,122)(58,121)(59,120)(60,119)(61,118)(62,117)(63,116)(64,115)(65,114)(66,113)(67,112)(68,111)(69,110)(70,109)(71,108)(72,107)(73,106)(74,105)(75,104)(76,103)(77,102)(78,101)(79,100)(80,99)(81,98)(82,97)(83,96)(84,95)(85,94)(86,93)(87,92)(88,91)(89,90)

Conjugacy classes & character table

3716 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₄₈₅₂
maximal normal subgroup of	D₁₄₈₅₂
maximal quotient of	D₁₄₈₅₂, Dic₇₄₂₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14852, 7);

C2×D3713 #28415360