C₃₇×C₃⋊D₉ #14522012

order	1998
isoclinism	isoclinic class of C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃₇×C₃⋊D₉
unambiguous semidirect product	C₃⋊(D₉×C₃₇)
unambiguous semidirect product	C₉⋊(D₃×C₃₇)

Splittings

Fitting, Hall	C₃×C₉×C₃₇ ⋊ C₂
derived, Sylow	C₃×C₉ ⋊ C₂×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃₇	C₃⋊D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₃₇
Frattini	C₃	C₃⋊D₃×C₃₇
Fitting	C₃×C₉×C₃₇	C₂
socle	C₃²×C₃₇	D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₃₇

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 999

A minimal faithful permutation representation — 3 generators on 49 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)(39,40)(42,44)(43,47)(45,46)(48,49);(38,39,40);(41,49,44,47,46,45,43,42,48)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1998, 42);

C37×C3⋊D9 #14522012