C₂×D₄²×C₃₇ #17992280

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product

C₂×D₄²×C₃₇

Subgroups

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

2536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 generators on 47 points:

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

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8375, C₃₇×#8383, C₃₇×#8443, …
maximal normal subgroup of	C₃₇×#8375, C₃₇×#8383, C₃₇×#8443, …
maximal quotient of	C₂×D₄×C₂²⋊C₄×C₃₇, C₂×D₄×C₄⋊C₄×C₃₇, C₂×C₃₇×#2358, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2194);

C2×D42×C37 #17992280