D₃₉×C₁₆₇ #27189307

order	13026
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃₉×C₁₆₇
unambiguous semidirect product	C₃⋊(D₁₃×C₁₆₇)
unambiguous semidirect product	C₁₃⋊(D₃×C₁₆₇)

Splittings

Fitting, socle, Hall	C₃×C₁₃×C₁₆₇ ⋊ C₂
derived, Hall	C₃×C₁₃ ⋊ C₂×C₁₆₇
Hall	C₁₃×C₁₆₇ ⋊ D₃
Hall	C₃×C₁₆₇ ⋊ D₁₃
Sylow	C₁₃ ⋊ D₃×C₁₆₇
Sylow	C₃ ⋊ D₁₃×C₁₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₆₇	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₁₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₆₇	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₁₆₇

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 183
transitive degree	μ_t(G) = 6513

A minimal faithful permutation representation — 2 generators on 183 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,16)

Conjugacy classes & character table

3507 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₉×D₁₆₇, D₃×D₁₃×C₁₆₇, D₃₉⋊D₁₆₇, …
maximal normal subgroup of	D₃₉×D₁₆₇, D₃×D₁₃×C₁₆₇, D₃₉⋊D₁₆₇, …
maximal quotient of	Dic₃₉×C₁₆₇, C₂×D₃₉×C₁₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13026, 8);

D39×C167 #27189307