C₂×D₅₇₃₃ #37524131

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₁₄₆₆
direct product	C₂×D₅₇₃₃
unambiguous semidirect product	(C₂×C₉)⋊D₆₃₇
unambiguous semidirect product	(C₂×C₁₃)⋊D₄₄₁
unambiguous semidirect product	(C₂×C₄₉)⋊D₁₁₇

Splittings

Fitting	C₂×C₉×C₁₃×C₄₉ ⋊ C₂
derived, Hall	C₉×C₁₃×C₄₉ ⋊ C₂²
Hall	C₁₃×C₄₉ ⋊ C₂×D₉
Hall	C₉×C₄₉ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₁₁₇
Sylow	C₁₃ ⋊ C₂×D₄₄₁
Sylow	C₉ ⋊ C₂×D₆₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₅₇₃₃
commutator, cosocle, hypocenter	C₉×C₁₃×C₄₉	C₂²
Frattini	C₃×C₇	C₂×D₂₇₃
Fitting	C₂×C₉×C₁₃×C₄₉	C₂
socle	C₂×C₃×C₇×C₁₃	D₂₁
LCS	G ▷ C₉×C₁₃×C₄₉
UCS	C₁ ◁ C₂

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 11466

A minimal faithful permutation representation — 2 generators on 73 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);(4,11)(5,10)(6,9)(7,8)(13,60)(14,59)(15,58)(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(62,73)(63,72)(64,71)(65,70)(66,69)(67,68)

Conjugacy classes & character table

5736 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₂₉₃₂
maximal normal subgroup of	D₂₂₉₃₂
maximal quotient of	Dic₁₁₄₆₆, D₂₂₉₃₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 76);

C2×D5733 #37524131