C₂×D₆₂₀₁ #37613626

order	24804
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₂₄₀₂
direct product	C₂×D₆₂₀₁
unambiguous semidirect product	(C₂×C₉)⋊D₆₈₉
unambiguous semidirect product	(C₂×C₁₃)⋊D₄₇₇
unambiguous semidirect product	(C₂×C₅₃)⋊D₁₁₇

Splittings

Fitting	C₂×C₉×C₁₃×C₅₃ ⋊ C₂
derived, Hall	C₉×C₁₃×C₅₃ ⋊ C₂²
Hall	C₁₃×C₅₃ ⋊ C₂×D₉
Hall	C₉×C₅₃ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₅₃
Sylow	C₅₃ ⋊ C₂×D₁₁₇
Sylow	C₁₃ ⋊ C₂×D₄₇₇
Sylow	C₉ ⋊ C₂×D₆₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₆₂₀₁
commutator, cosocle, hypocenter	C₉×C₁₃×C₅₃	C₂²
Frattini	C₃	C₂×D₂₀₆₇
Fitting	C₂×C₉×C₁₃×C₅₃	C₂
socle	C₂×C₃×C₁₃×C₅₃	D₃
LCS	G ▷ C₉×C₁₃×C₅₃
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 12402

A minimal faithful permutation representation — 2 generators on 77 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)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(4,11)(5,10)(6,9)(7,8)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

6204 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₄₈₀₄
maximal normal subgroup of	D₂₄₈₀₄
maximal quotient of	Dic₁₂₄₀₂, D₂₄₈₀₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 58);

C2×D6201 #37613626