C₃₇⋊C₃×#64418 #45657383

order	32634
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇⋊C₃×#64418

Splittings

Fitting, socle, Hall	C₇²×C₃₇ ⋊ C₃×D₃
derived	C₃₇×#3862 ⋊ C₂×C₃
Hall	C₃₇⋊C₃×#3862 ⋊ C₂
Sylow	C₇² ⋊ D₃×C₃₇⋊C₃
Sylow	C₃₇ ⋊ C₃×#64418

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃₇×#3862	C₂×C₃
Fitting, socle	C₇²×C₃₇	C₃×D₃
LCS	G ▷ C₃₇×#3862
UCS	C₁

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 518

A minimal faithful permutation representation — 2 generators on 51 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32634, 163);

C37⋊C3×#64418 #45657383