C₂×C₃₇×#577 #17992400

order	4736
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×C₃₇×#577

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₃₇
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 generators on 55 points:

(1,2)(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);(3,4,7,11)(5,9,12,16)(6,8,14,10)(13,15,18,17);(4,8)(6,14)(9,15)(10,11)(13,18)(16,17);(3,5)(4,9)(6,13)(7,12)(8,15)(10,17)(11,16)(14,18);(5,12)(9,16)(13,18)(15,17)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#22456, C₃₇×#22459, C₃₇×#22464, …
maximal normal subgroup of	C₃₇×#22456, C₃₇×#22459, C₃₇×#22464, …
maximal quotient of	C₂×C₃₇×#2897, C₂×C₃₇×#2898, C₂×C₃₇×#2912, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2314);

C2×C37×#577 #17992400