C₂×D₉₀₁ #16813362

order	3604
automorphism	Aut(G) order 1499264
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₀₂
direct product	C₂×D₉₀₁
unambiguous semidirect product	(C₂×C₁₇)⋊D₅₃
unambiguous semidirect product	(C₂×C₅₃)⋊D₁₇

Splittings

Fitting, socle	C₂×C₁₇×C₅₃ ⋊ C₂
derived, Hall	C₁₇×C₅₃ ⋊ C₂²
Sylow	C₅₃ ⋊ C₂×D₁₇
Sylow	C₁₇ ⋊ C₂×D₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₀₁
commutator, cosocle, hypocenter	C₁₇×C₅₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₇×C₅₃	C₂
LCS	G ▷ C₁₇×C₅₃
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 1802

A minimal faithful permutation representation — 2 generators on 72 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);(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(21,72)(22,71)(23,70)(24,69)(25,68)(26,67)(27,66)(28,65)(29,64)(30,63)(31,62)(32,61)(33,60)(34,59)(35,58)(36,57)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51)(43,50)(44,49)(45,48)(46,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×D₉₀₁, C₂×D₂₇₀₃, C₂×C₃×D₉₀₁, …
maximal normal subgroup of	C₂×C₃×D₉₀₁, C₂×C₅×D₉₀₁, C₂×C₇×D₉₀₁, …
maximal quotient of	D₃×D₉₀₁, C₂×D₂₇₀₃, C₂×C₃×D₉₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3604, 13);

C2×D901 #16813362