C₅₃×C₁₂₇⋊C₃ #34118458

order	20193
isoclinism	isoclinic class of C₁₂₇⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₃×C₁₂₇⋊C₃
unambiguous semidirect product	C₁₂₇⋊(C₃×C₅₃)
unambiguous semidirect product	(C₅₃×C₁₂₇)⋊C₃

Splittings

Fitting, socle, Hall	C₅₃×C₁₂₇ ⋊ C₃
derived, Sylow	C₁₂₇ ⋊ C₃×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅₃	C₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₁₂₇	C₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₅₃×C₁₂₇	C₃
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₅₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 180
transitive degree	μ_t(G) = 6731

A minimal faithful permutation representation — 2 generators on 180 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,69)(41,55,66)(44,58,63)(47,61,60)(50,64,57)(52,67,54)(56,72,85)(59,74,82)(62,77,79)(65,80,76)(68,83,73)(70,86,71)(75,89,99)(78,91,96)(81,94,93)(84,97,90)(87,100,88)(92,103,110)(95,105,107)(98,108,104)(101,111,102)(106,114,118)(109,116,115)(112,119,113)(117,122,123)(120,124,121)(125,127,126)(128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180);(1,2,4,8,15,25,38,53,70,87,101,112,120,125,124,108,80,46,20,5,9,16,26,39,54,71,72,37,52,68,84,98,109,117,119,97,64,33,12,19,29,42,57,73,88,89,55,24,36,50,65,81,95,106,111,83,49,22,32,45,60,76,90,102,103,74,40,14,23,34,47,62,78,92,100,67,35,48,63,79,93,104,113,114,91,58,27,7,13,21,31,44,59,75,86,51,66,82,96,107,115,121,122,105,77,43,17,3,6,11,18,28,41,56,69,85,99,110,118,123,126,127,116,94,61,30,10)

Conjugacy classes & character table

2385 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20193, 1);

C53×C127⋊C3 #34118458