C₅×C₂³⋊C₄₉ #14519936

order	1960
isoclinism	isoclinic class of AGL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₅×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂³⋊C₄₉
unambiguous semidirect product	C₂³⋊(C₅×C₄₉)
unambiguous semidirect product	(C₂³×C₅)⋊C₄₉

Splittings

derived, Sylow	C₂³ ⋊ C₅×C₄₉
Hall	C₂³×C₅ ⋊ C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₇	AGL(1,𝔽₈)
commutator, hypocenter	C₂³	C₅×C₄₉
Frattini	C₇	C₅×AGL(1,𝔽₈)
Fitting, socle, prime radical	C₂³×C₅×C₇	C₇
cosocle	C₂³×C₇	C₅×C₇
LCS	G ▷ C₂³
UCS	C₁ ◁ C₅×C₇

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 490

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2,3,4,5)(7,8,9,11,13,10,12)(14,15,17,20,24,29,35,16,18,21,25,30,36,42,19,22,26,31,37,43,48,23,27,32,38,44,49,53,28,33,39,45,50,54,57,34,40,46,51,55,58,60,41,47,52,56,59,61,62);(6,10)(7,8)(9,13)(11,12)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 33);

C5×C23⋊C49 #14519936