C₂×D₆₀₀₃ #37562160

order	24012
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₂₀₀₆
direct product	C₂×D₆₀₀₃
unambiguous semidirect product	(C₂×C₉)⋊D₆₆₇
unambiguous semidirect product	(C₂×C₂₃)⋊D₂₆₁
unambiguous semidirect product	(C₂×C₂₉)⋊D₂₀₇

Splittings

Fitting	C₂×C₉×C₂₃×C₂₉ ⋊ C₂
derived, Hall	C₉×C₂₃×C₂₉ ⋊ C₂²
Hall	C₂₃×C₂₉ ⋊ C₂×D₉
Hall	C₉×C₂₉ ⋊ C₂×D₂₃
Hall	C₉×C₂₃ ⋊ C₂×D₂₉
Sylow	C₂₉ ⋊ C₂×D₂₀₇
Sylow	C₂₃ ⋊ C₂×D₂₆₁
Sylow	C₉ ⋊ C₂×D₆₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₆₀₀₃
commutator, cosocle, hypocenter	C₉×C₂₃×C₂₉	C₂²
Frattini	C₃	C₂×D₂₀₀₁
Fitting	C₂×C₉×C₂₃×C₂₉	C₂
socle	C₂×C₃×C₂₃×C₂₉	D₃
LCS	G ▷ C₉×C₂₃×C₂₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 12006

A minimal faithful permutation representation — 2 generators on 63 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);(4,11)(5,10)(6,9)(7,8)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Conjugacy classes & character table

6006 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₄₀₁₂
maximal normal subgroup of	D₂₄₀₁₂
maximal quotient of	Dic₁₂₀₀₆, D₂₄₀₁₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24012, 22);

C2×D6003 #37562160