C₃₇×#2248 #17991066

order	4736
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₇×#2248

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₇
prime radical	C₃₇×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 3 generators on 57 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)(39,41)(43,47)(44,51)(45,52)(48,53)(49,57)(50,56)(54,55);(42,43,48,57,45,49,44,47,46,50,51,55,52,54,53,56);(38,39,40,41)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12318, C₃₇×#12319, C₃₇×#12320, …
maximal normal subgroup of	C₃₇×#12318, C₃₇×#12319, C₃₇×#12320, …
maximal quotient of	C₃₇×#12505, C₃₇×#12509, C₃₇×#12510, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 980);

C37×#2248 #17991066