C₃₇×#168 #13093306

order	1480
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₈×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×#168

Splittings

derived, Sylow	C₅ ⋊ C₈×C₃₇
Hall	C₅×C₃₇ ⋊ C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₃₇	D₅
commutator, hypocenter	C₅	C₈×C₃₇
Frattini	C₄	D₅×C₃₇
Fitting	C₄×C₅×C₃₇	C₂
socle, prime radical	C₂×C₅×C₃₇	C₄
cosocle	C₄×C₅	C₂×C₃₇
LCS	G ▷ C₅
UCS	C₁ ◁ C₄×C₃₇

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 1480

A minimal faithful permutation representation — 2 generators on 50 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)(39,40)(41,42)(43,44,45,47,46,48,49,50);(38,39,41,42,40)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1480, 1);

C37×#168 #13093306