C₂×D₄₅₇₅ #32912947

order	18300
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₉₁₅₀
direct product	C₂×D₄₅₇₅
unambiguous semidirect product	(C₂×C₃)⋊D₁₅₂₅
unambiguous semidirect product	(C₂×C₂₅)⋊D₁₈₃
unambiguous semidirect product	(C₂×C₆₁)⋊D₇₅

Splittings

Fitting	C₂×C₃×C₂₅×C₆₁ ⋊ C₂
derived, Hall	C₃×C₂₅×C₆₁ ⋊ C₂²
Hall	C₂₅×C₆₁ ⋊ C₂×D₃
Hall	C₃×C₆₁ ⋊ C₂×D₂₅
Hall	C₃×C₂₅ ⋊ C₂×D₆₁
Sylow	C₆₁ ⋊ C₂×D₇₅
Sylow	C₂₅ ⋊ C₂×D₁₈₃
Sylow	C₃ ⋊ C₂×D₁₅₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₅₇₅
commutator, cosocle, hypocenter	C₃×C₂₅×C₆₁	C₂²
Frattini	C₅	C₂×D₉₁₅
Fitting	C₂×C₃×C₂₅×C₆₁	C₂
socle	C₂×C₃×C₅×C₆₁	D₅
LCS	G ▷ C₃×C₂₅×C₆₁
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 9150

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

Conjugacy classes & character table

4578 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₈₃₀₀, C₂×D₁₃₇₂₅
maximal normal subgroup of	D₁₈₃₀₀
maximal quotient of	Dic₉₁₅₀, D₁₈₃₀₀, C₂×D₁₃₇₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 70);

C2×D4575 #32912947