C₂×D₆₀₂₇ #37563033

order	24108
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₂₀₅₄
direct product	C₂×D₆₀₂₇
unambiguous semidirect product	(C₂×C₃)⋊D₂₀₀₉
unambiguous semidirect product	(C₂×C₄₁)⋊D₁₄₇
unambiguous semidirect product	(C₂×C₄₉)⋊D₁₂₃

Splittings

Fitting	C₂×C₃×C₄₁×C₄₉ ⋊ C₂
derived, Hall	C₃×C₄₁×C₄₉ ⋊ C₂²
Hall	C₄₁×C₄₉ ⋊ C₂×D₃
Hall	C₃×C₄₉ ⋊ C₂×D₄₁
Hall	C₃×C₄₁ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₁₂₃
Sylow	C₄₁ ⋊ C₂×D₁₄₇
Sylow	C₃ ⋊ C₂×D₂₀₀₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₆₀₂₇
commutator, cosocle, hypocenter	C₃×C₄₁×C₄₉	C₂²
Frattini	C₇	C₂×D₈₆₁
Fitting	C₂×C₃×C₄₁×C₄₉	C₂
socle	C₂×C₃×C₇×C₄₁	D₇
LCS	G ▷ C₃×C₄₁×C₄₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 12054

A minimal faithful permutation representation — 2 generators on 95 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)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(4,5)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(56,95)(57,94)(58,93)(59,92)(60,91)(61,90)(62,89)(63,88)(64,87)(65,86)(66,85)(67,84)(68,83)(69,82)(70,81)(71,80)(72,79)(73,78)(74,77)(75,76)

Conjugacy classes & character table

6030 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₄₁₀₈
maximal normal subgroup of	D₂₄₁₀₈
maximal quotient of	Dic₁₂₀₅₄, D₂₄₁₀₈

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24108, 40);

C2×D6027 #37563033