C₅×C₂₃×D₁₇ #16840933

order	3910
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₃×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₅×C₂₃)

Splittings

Fitting, socle, Hall	C₅×C₁₇×C₂₃ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₅×C₂₃
Hall	C₁₇×C₂₃ ⋊ C₂×C₅
Hall	C₅×C₁₇ ⋊ C₂×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₂₃	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₂₃	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₅×C₂₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1955

A minimal faithful permutation representation — 2 generators on 45 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);(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅×C₂₃×D₁₇, C₅×C₂₃×D₅₁, C₂₃×C₂₅×D₁₇, …
maximal normal subgroup of	C₃×C₅×C₂₃×D₁₇, C₂₃×C₂₅×D₁₇, C₅²×C₂₃×D₁₇, …
maximal quotient of	C₃×C₅×C₂₃×D₁₇, C₅×C₂₃×D₅₁, C₂₃×C₂₅×D₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3910, 3);

C5×C23×D17 #16840933