C₁₇×#2843 #14525849

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2843

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

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

normal subgroups only

This group has 348 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) = 41
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 4 generators on 41 points:

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946913, #16947397, D₁₇×#2843, …
maximal subgroup of	C₁₇×#12183, C₁₇×#12259, C₂×C₁₇×#2843, …
maximal normal subgroup of	C₁₇×#12183, C₁₇×#12259, C₂×C₁₇×#2843, …
maximal quotient of	C₁₇×#14638, C₁₇×#14639, C₁₇×#14640, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1575);