C₁₆×Dic₂₀₂ #27173035

order	12928
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₆×Dic₂₀₂

Splittings

Sylow

C₁₀₁ ⋊ Q₈×C₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₆	C₂×D₁₀₁
commutator	C₂×C₁₀₁	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×D₁₀₁
Fitting	C₄×C₁₆×C₁₀₁	C₂
socle, prime radical	C₂²×C₁₀₁	C₂²×C₈
cosocle	C₂×C₈×C₁₀₁	C₂³
hypercenter	C₄×C₁₆	D₁₀₁
hypocenter	C₁₀₁	Q₈×C₁₆
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 3 generators on 125 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(102,104,105,109)(103,106,107,108);(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)(102,103,105,107)(104,108,109,106);(110,111,112,115,113,116,118,121,114,117,119,122,120,123,124,125)

Conjugacy classes & character table

3280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 6413);

C16×Dic202 #27173035