C₃₇×#2988 #17991806

order	4736
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#2988

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁴
commutator	C₂	C₂³×C₈×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂³×C₄
prime radical	C₂×#41×C₃₇	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(39,42)(40,44)(46,47,48,50,49,51,52,53);(38,39)(40,43)(41,42)(44,45);(39,42)(43,45);(38,40,41,44)(39,43,42,45)

Conjugacy classes & character table

2516 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8839, C₃₇×#8840, C₃₇×#8953, …
maximal normal subgroup of	C₃₇×#8839, C₃₇×#8840, C₃₇×#8953, …
maximal quotient of	C₃₇×#20543, C₃₇×#20555, C₃₇×#20569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1720);

C37×#2988 #17991806