C₂×D₄₉₇₇ #34092603

order	19908
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₉₉₅₄
direct product	C₂×D₄₉₇₇
unambiguous semidirect product	(C₂×C₇)⋊D₇₁₁
unambiguous semidirect product	(C₂×C₉)⋊D₅₅₃
unambiguous semidirect product	(C₂×C₇₉)⋊D₆₃

Splittings

Fitting	C₂×C₇×C₉×C₇₉ ⋊ C₂
derived, Hall	C₇×C₉×C₇₉ ⋊ C₂²
Hall	C₉×C₇₉ ⋊ C₂×D₇
Hall	C₇×C₇₉ ⋊ C₂×D₉
Sylow	C₇₉ ⋊ C₂×D₆₃
Hall	C₇×C₉ ⋊ C₂×D₇₉
Sylow	C₉ ⋊ C₂×D₅₅₃
Sylow	C₇ ⋊ C₂×D₇₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₉₇₇
commutator, cosocle, hypocenter	C₇×C₉×C₇₉	C₂²
Frattini	C₃	C₂×D₁₆₅₉
Fitting	C₂×C₇×C₉×C₇₉	C₂
socle	C₂×C₃×C₇×C₇₉	D₃
LCS	G ▷ C₇×C₉×C₇₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 9954

A minimal faithful permutation representation — 2 generators on 97 points:

(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(4,11)(5,10)(6,9)(7,8)(13,18)(14,17)(15,16)(20,97)(21,96)(22,95)(23,94)(24,93)(25,92)(26,91)(27,90)(28,89)(29,88)(30,87)(31,86)(32,85)(33,84)(34,83)(35,82)(36,81)(37,80)(38,79)(39,78)(40,77)(41,76)(42,75)(43,74)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)(57,60)(58,59)

Conjugacy classes & character table

4980 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₉₉₀₈, C₂×D₁₄₉₃₁
maximal normal subgroup of	D₁₉₉₀₈
maximal quotient of	Dic₉₉₅₄, D₁₉₉₀₈, C₂×D₁₄₉₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19908, 64);

C2×D4977 #34092603