D₆₄₈₃ #27188397

order	12966
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₆₄₈₃
unambiguous semidirect product	C₃⋊D₂₁₆₁
unambiguous semidirect product	C₂₁₆₁⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₂₁₆₁ ⋊ C₂
Sylow	C₂₁₆₁ ⋊ D₃
Sylow	C₃ ⋊ D₂₁₆₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₂₁₆₁	C₂
LCS	G ▷ C₃×C₂₁₆₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2164
transitive degree	μ_t(G) = 6483

A minimal faithful permutation representation — 2 generators on 2164 points:

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(1039,1130)(1040,1129)(1041,1128)(1042,1127)(1043,1126)(1044,1125)(1045,1124)(1046,1123)(1047,1122)(1048,1121)(1049,1120)(1050,1119)(1051,1118)(1052,1117)(1053,1116)(1054,1115)(1055,1114)(1056,1113)(1057,1112)(1058,1111)(1059,1110)(1060,1109)(1061,1108)(1062,1107)(1063,1106)(1064,1105)(1065,1104)(1066,1103)(1067,1102)(1068,1101)(1069,1100)(1070,1099)(1071,1098)(1072,1097)(1073,1096)(1074,1095)(1075,1094)(1076,1093)(1077,1092)(1078,1091)(1079,1090)(1080,1089)(1081,1088)(1082,1087)(1083,1086)(1084,1085)

Polycyclic presentation:

2,3,2161|b^a=b^2,c^a=c^2160

Conjugacy classes & character table

3243 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₂₁₆₁, C₂×D₆₄₈₃
maximal normal subgroup of	D₃×D₂₁₆₁, C₂×D₆₄₈₃
maximal quotient of	Dic₆₄₈₃, C₂×D₆₄₈₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12966, 5);

D6483 #27188397