C₁₇×D₃₇ #11929445

order	1258
isoclinism	isoclinic class of D₃₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₃₇
unambiguous semidirect product	C₃₇⋊(C₂×C₁₇)

Splittings

Fitting, socle, Hall	C₁₇×C₃₇ ⋊ C₂
derived, Sylow	C₃₇ ⋊ C₂×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₃₇	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₁₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 629

A minimal faithful permutation representation — 2 generators on 54 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);(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₇×#3866, #14578982, D₁₇×D₃₇, …
maximal normal subgroup of	C₁₇×#3866, #14578982, D₁₇×D₃₇, …
maximal quotient of	C₁₇×Dic₃₇, C₂×C₁₇×D₃₇, C₃×C₁₇×D₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1258, 2);

C17×D37 #11929445