C₁₇×#2097 #14525103

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

Aliases

direct product

C₁₇×#2097

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

238 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 45
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 45 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)(30,31,33,37,34,38,42,35)(32,39,40,44,41,45,43,36);(18,19)(20,21)(22,24,25,29)(23,26,27,28)(31,35)(33,42)(36,39)(37,38)(40,43)(44,45);(19,21)(30,32,34,41)(31,36,38,44)(33,43,42,40)(35,39,37,45)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2097, #17064123, #17064138, …
maximal subgroup of	C₂×C₁₇×#2097, C₁₇×#23730, C₁₇×#23732, …
maximal normal subgroup of	C₂×C₁₇×#2097, C₁₇×#23730, C₁₇×#23732, …
maximal quotient of	C₁₇×#10664, C₁₇×#10669, C₁₇×#10675, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 829);