C₂×C₃₇×#498 #17991975

order	4736
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂×C₃₇×#498

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 4 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);(3,4,6,8)(5,9,10,7)(12,15)(13,17)(16,18);(3,5,6,10)(4,7,8,9);(11,12,13,15,14,16,17,18)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9059, C₃₇×#9729, C₃₇×#9741, …
maximal normal subgroup of	C₃₇×#9059, C₃₇×#9729, C₃₇×#9741, …
maximal quotient of	C₂×C₃₇×#1844, C₂×C₃₇×#1941, C₂×C₃₇×#1990, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1889);

C2×C37×#498 #17991975