C₁₀₇×D₅₉ #27162256

order	12626
isoclinism	isoclinic class of D₅₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₀₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₀₇×D₅₉
unambiguous semidirect product	C₅₉⋊(C₂×C₁₀₇)

Splittings

Fitting, socle, Hall	C₅₉×C₁₀₇ ⋊ C₂
derived, Sylow	C₅₉ ⋊ C₂×C₁₀₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₀₇	D₅₉
commutator, cosocle, hypocenter	C₅₉	C₂×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₅₉×C₁₀₇	C₂
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₁₀₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 166
transitive degree	μ_t(G) = 6313

A minimal faithful permutation representation — 2 generators on 166 points:

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

Conjugacy classes & character table

3317 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅₉×D₁₀₇, C₂×C₁₀₇×D₅₉, C₃×C₁₀₇×D₅₉, …
maximal normal subgroup of	D₅₉×D₁₀₇, C₂×C₁₀₇×D₅₉, C₃×C₁₀₇×D₅₉
maximal quotient of	C₁₀₇×Dic₅₉, C₂×C₁₀₇×D₅₉, C₃×C₁₀₇×D₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12626, 1);

C107×D59 #27162256