C₂×D₃₆₄₉ #28410254

order	14596
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₇₂₉₈
direct product	C₂×D₃₆₄₉
unambiguous semidirect product	(C₂×C₄₁)⋊D₈₉
unambiguous semidirect product	(C₂×C₈₉)⋊D₄₁

Splittings

Fitting, socle	C₂×C₄₁×C₈₉ ⋊ C₂
derived, Hall	C₄₁×C₈₉ ⋊ C₂²
Sylow	C₈₉ ⋊ C₂×D₄₁
Sylow	C₄₁ ⋊ C₂×D₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₃₆₄₉
commutator, cosocle, hypocenter	C₄₁×C₈₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₄₁×C₈₉	C₂
LCS	G ▷ C₄₁×C₈₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 132
transitive degree	μ_t(G) = 7298

A minimal faithful permutation representation — 2 generators on 132 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)(44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132);(4,43)(5,42)(6,41)(7,40)(8,39)(9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(45,132)(46,131)(47,130)(48,129)(49,128)(50,127)(51,126)(52,125)(53,124)(54,123)(55,122)(56,121)(57,120)(58,119)(59,118)(60,117)(61,116)(62,115)(63,114)(64,113)(65,112)(66,111)(67,110)(68,109)(69,108)(70,107)(71,106)(72,105)(73,104)(74,103)(75,102)(76,101)(77,100)(78,99)(79,98)(80,97)(81,96)(82,95)(83,94)(84,93)(85,92)(86,91)(87,90)(88,89)

Conjugacy classes & character table

3652 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₄₅₉₆
maximal normal subgroup of	D₁₄₅₉₆
maximal quotient of	D₁₄₅₉₆, Dic₇₂₉₈

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14596, 13);

C2×D3649 #28410254