C₁₇×C₃⋊C₃₂ #13108666

order	1632
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₁₇×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₃⋊C₃₂
unambiguous semidirect product	C₃⋊(C₁₇×C₃₂)

Splittings

derived, Sylow	C₃ ⋊ C₁₇×C₃₂
Hall	C₃×C₁₇ ⋊ C₃₂

Subgroups

	subgroup	G/H
center, hypercenter	C₁₆×C₁₇	D₃
commutator, hypocenter	C₃	C₁₇×C₃₂
Frattini	C₁₆	D₃×C₁₇
Fitting	C₃×C₁₆×C₁₇	C₂
socle, prime radical	C₂×C₃×C₁₇	C₁₆
cosocle	C₃×C₁₆	C₂×C₁₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₆×C₁₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 1632

A minimal faithful permutation representation — 2 generators on 52 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(21,22,23,27,24,28,31,37,25,29,32,38,34,40,43,47,26,30,33,39,35,41,44,48,36,42,45,49,46,50,51,52);(18,19,20)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1632, 1);

C17×C3⋊C32 #13108666