#168×C₄₉ #14519904

order	1960
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₈×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

#168×C₄₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₄₉	D₅
commutator, hypocenter	C₅	C₈×C₄₉
Frattini	C₄×C₇	C₇×D₅
Fitting	C₄×C₅×C₄₉	C₂
socle, prime radical	C₂×C₅×C₇	C₄×C₇
cosocle	C₄×C₅×C₇	C₂×C₇
LCS	G ▷ C₅
UCS	C₁ ◁ C₄×C₄₉

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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 1);

#168×C49 #14519904