C₅×C₄₉⋊C₈ #14519905

order	1960
isoclinism	isoclinic class of D₄₉
automorphism	?
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₄₉⋊C₈
unambiguous semidirect product	C₄₉⋊(C₅×C₈)

Splittings

derived, Sylow	C₄₉ ⋊ C₅×C₈
Hall	C₅×C₄₉ ⋊ C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₅	D₄₉
commutator, hypocenter	C₄₉	C₅×C₈
Frattini	C₄×C₇	C₅×D₇
Fitting	C₄×C₅×C₄₉	C₂
socle, prime radical	C₂×C₅×C₇	Dic₇
cosocle	C₄×C₄₉	C₂×C₅
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₄×C₅

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 1960

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 2);

C5×C49⋊C8 #14519905