C₂×D₅₄₉₉ #36347193

order	21996
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₀₉₉₈
direct product	C₂×D₅₄₉₉
unambiguous semidirect product	(C₂×C₉)⋊D₆₁₁
unambiguous semidirect product	(C₂×C₁₃)⋊D₄₂₃
unambiguous semidirect product	(C₂×C₄₇)⋊D₁₁₇

Splittings

Fitting	C₂×C₉×C₁₃×C₄₇ ⋊ C₂
derived, Hall	C₉×C₁₃×C₄₇ ⋊ C₂²
Hall	C₁₃×C₄₇ ⋊ C₂×D₉
Hall	C₉×C₄₇ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×D₁₁₇
Sylow	C₁₃ ⋊ C₂×D₄₂₃
Sylow	C₉ ⋊ C₂×D₆₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₅₄₉₉
commutator, cosocle, hypocenter	C₉×C₁₃×C₄₇	C₂²
Frattini	C₃	C₂×D₁₈₃₃
Fitting	C₂×C₉×C₁₃×C₄₇	C₂
socle	C₂×C₃×C₁₃×C₄₇	D₃
LCS	G ▷ C₉×C₁₃×C₄₇
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 10998

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

Conjugacy classes & character table

5502 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₁₉₉₆
maximal normal subgroup of	D₂₁₉₉₆
maximal quotient of	Dic₁₀₉₉₈, D₂₁₉₉₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 34);

C2×D5499 #36347193