C₁₇×D₁₀₇ #16813932

order	3638
isoclinism	isoclinic class of D₁₀₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₁₀₇
unambiguous semidirect product	C₁₀₇⋊(C₂×C₁₇)

Splittings

Fitting, socle, Hall	C₁₇×C₁₀₇ ⋊ C₂
derived, Sylow	C₁₀₇ ⋊ C₂×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₁₀₇
commutator, cosocle, hypocenter	C₁₀₇	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₁₀₇	C₂
LCS	G ▷ C₁₀₇
UCS	C₁ ◁ C₁₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 124
transitive degree	μ_t(G) = 1819

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₁₇×D₁₀₇, C₁₇×D₃₂₁, C₅×C₁₇×D₁₀₇, …
maximal normal subgroup of	C₃×C₁₇×D₁₀₇, C₅×C₁₇×D₁₀₇, C₇×C₁₇×D₁₀₇
maximal quotient of	C₃×C₁₇×D₁₀₇, C₁₇×D₃₂₁, C₅×C₁₇×D₁₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3638, 2);

C17×D107 #16813932