C₂×D₈₀₃₇ #44565268

order	32148
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₆₀₇₄
direct product	C₂×D₈₀₃₇
unambiguous semidirect product	(C₂×C₉)⋊D₈₉₃
unambiguous semidirect product	(C₂×C₁₉)⋊D₄₂₃
unambiguous semidirect product	(C₂×C₄₇)⋊D₁₇₁

Splittings

Fitting	C₂×C₉×C₁₉×C₄₇ ⋊ C₂
derived, Hall	C₉×C₁₉×C₄₇ ⋊ C₂²
Hall	C₁₉×C₄₇ ⋊ C₂×D₉
Hall	C₉×C₄₇ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×D₁₇₁
Sylow	C₁₉ ⋊ C₂×D₄₂₃
Sylow	C₉ ⋊ C₂×D₈₉₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₀₃₇
commutator, cosocle, hypocenter	C₉×C₁₉×C₄₇	C₂²
Frattini	C₃	C₂×D₂₆₇₉
Fitting	C₂×C₉×C₁₉×C₄₇	C₂
socle	C₂×C₃×C₁₉×C₄₇	D₃
LCS	G ▷ C₉×C₁₉×C₄₇
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 16074

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)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(32,77)(33,76)(34,75)(35,74)(36,73)(37,72)(38,71)(39,70)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)

Conjugacy classes & character table

8040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₂₁₄₈
maximal normal subgroup of	D₃₂₁₄₈
maximal quotient of	Dic₁₆₀₇₄, D₃₂₁₄₈

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 28);

C2×D8037 #44565268