D₁₇×C₁₂₇ #16864458

order	4318
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₂₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₇×C₁₂₇
unambiguous semidirect product	C₁₇⋊(C₂×C₁₂₇)

Splittings

Fitting, socle, Hall	C₁₇×C₁₂₇ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₁₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₂₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₁₂₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₁₂₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 144
transitive degree	μ_t(G) = 2159

A minimal faithful permutation representation — 2 generators on 144 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)

Conjugacy classes & character table

1270 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₁₇×C₁₂₇, D₅₁×C₁₂₇, D₁₇×C₁₂₇⋊C₃, …
maximal normal subgroup of	C₃×D₁₇×C₁₂₇, D₁₇×C₁₂₇⋊C₃, C₅×D₁₇×C₁₂₇, …
maximal quotient of	C₃×D₁₇×C₁₂₇, D₅₁×C₁₂₇, C₅×D₁₇×C₁₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4318, 1);

D17×C127 #16864458