D₁₃×C₁₂₇ #15693237

order	3302
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₂₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₃×C₁₂₇
unambiguous semidirect product	C₁₃⋊(C₂×C₁₂₇)

Splittings

Fitting, socle, Hall	C₁₃×C₁₂₇ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₁₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₂₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₂₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₂₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 140
transitive degree	μ_t(G) = 1651

A minimal faithful permutation representation — 2 generators on 140 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)

Conjugacy classes & character table

1016 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₁₃×C₁₂₇, C₁₂₇×D₆₅, C₇×D₁₃×C₁₂₇, …
maximal normal subgroup of	C₅×D₁₃×C₁₂₇, C₇×D₁₃×C₁₂₇, D₁₃×C₁₂₇⋊C₇, …
maximal quotient of	C₅×D₁₃×C₁₂₇, C₁₂₇×D₆₅, C₇×D₁₃×C₁₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3302, 1);

D13×C127 #15693237