C₂×C₃₇×#366 #17990974

order	4736
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₃₇×#366

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇	D₈
commutator	C₈	C₂²×C₄×C₃₇
Frattini, cosocle	C₂×C₈	C₂³×C₃₇
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59);(3,4,5,6)(8,12)(9,13)(10,16)(14,22)(15,20)(17,21)(18,19);(7,8,13,19,10,14,17,20,11,15,21,22,16,18,9,12)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7471, C₃₇×#7478, C₄×C₃₇×#366, …
maximal normal subgroup of	C₃₇×#7471, C₃₇×#7478, C₄×C₃₇×#366, …
maximal quotient of	C₂×C₃₇×#1371, C₃₇×#12022, C₃₇×#12032, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 888);

C2×C37×#366 #17990974