C₁₇×#2096 #14525102

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2096

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

254 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 37
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,25,27)(24,28,29,26)(30,31,35,37,34,32,33,36);(18,19)(20,21)(22,24,25,29)(23,26,27,28)(30,32,34,31)(33,36,35,37);(19,21)(30,31,34,32)(33,37,35,36)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921936, #16923448, #16923454, …
maximal subgroup of	C₁₇×#7437, C₁₇×#7801, C₁₇×#7802, …
maximal normal subgroup of	C₁₇×#7437, C₁₇×#7801, C₁₇×#7802, …
maximal quotient of	C₁₇×#10663, C₁₇×#10670, C₁₇×#10675, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 828);