C₁₇×C₂₃×D₁₇ #27210830

order	13294
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

Fitting, socle, Hall	C₁₇²×C₂₃ ⋊ C₂
derived	C₁₇ ⋊ C₂×C₁₇×C₂₃
Sylow	C₁₇² ⋊ C₂×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇×C₂₃	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₁₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₁₇²×C₂₃	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₁₇×C₂₃

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 782

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(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);(18,19,21,23,25,27,29,31,33,34,32,30,28,26,24,22,20)

Conjugacy classes & character table

3910 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₇×D₁₇×D₂₃, C₁₇×C₂₃×#595, C₁₇×C₂₃⋊#595, …
maximal normal subgroup of	C₁₇×D₁₇×D₂₃, C₁₇×C₂₃×#595, C₁₇×C₂₃⋊#595, …
maximal quotient of	C₁₇×C₂₃×Dic₁₇, C₂×C₁₇×C₂₃×D₁₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13294, 9);

C17×C23×D17 #27210830