C₂×C₃₇×#538 #17992268

order	4736
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₃₇×#538

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

1336 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)(5,11)(6,10)(7,9)(8,12)(13,15)(14,17)(16,18);(3,5,7,13)(4,8,9,16)(6,12,14,18)(10,11,17,15);(4,9)(5,12)(8,15)(10,17)(11,16)(13,18);(4,10)(8,11)(9,17)(15,16)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8408, C₃₇×#17386, C₃₇×#17405, …
maximal normal subgroup of	C₃₇×#8408, C₃₇×#17386, C₃₇×#17405, …
maximal quotient of	C₂×C₃₇×#2312, C₂×C₃₇×#2318, C₂×C₃₇×#2321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2182);

C2×C37×#538 #17992268