C₁₇×#2822 #14525828

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2822

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

380 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 184 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 — 4 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(23,24)(27,28)(30,31,35,37)(32,38,40,33)(34,36,44,45)(39,43,42,41);(19,21)(22,23,26,24)(25,27,29,28)(30,32,35,40)(31,33,37,38)(34,42,44,39)(36,43,45,41);(18,19)(20,21)(22,24,26,23)(25,27,29,28)(30,33)(31,32)(34,43)(35,38)(36,42)(37,40)(39,45)(41,44);(22,25,26,29)(23,27,24,28)(30,34,35,44)(31,36,37,45)(32,39,40,42)(33,41,38,43)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16935615, #16935642, #16935660, …
maximal subgroup of	C₁₇×#10080, C₁₇×#10084, C₁₇×#10087, …
maximal normal subgroup of	C₁₇×#10080, C₁₇×#10084, C₁₇×#10087, …
maximal quotient of	C₁₇×#14629, C₁₇×#14631, C₁₇×#14634, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1554);