C₅×#67823 #14279274

order	1920
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#67823

Splittings

Hall	C₃×C₅ ⋊ #1401
Sylow	C₃ ⋊ C₅×#1401

Subgroups

	subgroup	G/H
center	C₅×C₁₆	#67
commutator	C₃×C₄	C₂×C₅×C₁₆
Frattini	C₂×C₁₆	C₂×C₅×D₃
Fitting	C₃×C₅×#504	C₂
socle	C₂×C₃×C₅	C₂²⋊C₁₆
prime radical	C₃×C₅×#41	C₈
cosocle	C₂×C₃×C₁₆	C₂²×C₅
hypercenter	C₅×#504	D₃
hypocenter	C₃	C₅×#1401
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₁₆ ◁ C₂×C₅×C₁₆ ◁ C₅×#504

144 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 2 generators on 72 points:

(1,2,3,4,5)(6,7,8)(9,11)(10,17)(12,28)(13,31)(14,26)(15,24)(16,27)(18,41)(19,44)(20,39)(21,23)(22,40)(25,34)(29,52)(30,56)(32,59)(33,37)(35,53)(36,55)(38,47)(42,50)(43,65)(45,67)(46,58)(48,51)(49,64)(54,61)(57,71)(60,62)(63,69)(66,70)(68,72);(7,8)(9,10,13,19,14,20,32,45,15,21,33,46,35,48,60,68,16,22,34,47,36,49,61,69,12,18,29,42,30,43,57,66)(11,23,25,50,26,51,54,70,24,40,52,44,53,64,71,67,27,41,31,58,55,65,59,72,28,17,37,38,56,39,62,63)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4972);