D₁₉×C₉₇ #16814769

order	3686
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₉₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₉×C₉₇
unambiguous semidirect product	C₁₉⋊(C₂×C₉₇)

Splittings

Fitting, socle, Hall	C₁₉×C₉₇ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₉₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉₇	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₉₇
Frattini	C₁	G
Fitting, socle	C₁₉×C₉₇	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₉₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 116
transitive degree	μ_t(G) = 1843

A minimal faithful permutation representation — 2 generators on 116 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);(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)

Conjugacy classes & character table

1067 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₁₉×C₉₇, C₉₇×D₅₇, D₁₉×C₉₇⋊C₃, …
maximal normal subgroup of	C₃×D₁₉×C₉₇, D₁₉×C₉₇⋊C₃, C₉₇×D₁₉⋊C₃, …
maximal quotient of	C₃×D₁₉×C₉₇, C₉₇×D₅₇, C₅×D₁₉×C₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3686, 1);

D19×C97 #16814769