C₅×#64436 #13093307

order	1480
isoclinism	isoclinic class of D₃₇
automorphism	?
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×#64436

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₅	D₃₇
commutator, hypocenter	C₃₇	C₅×C₈
Frattini	C₄	C₅×D₃₇
Fitting	C₄×C₅×C₃₇	C₂
socle, prime radical	C₂×C₅×C₃₇	C₄
cosocle	C₄×C₃₇	C₂×C₅
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₄×C₅

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1480, 2);

C5×#64436 #13093307