C₁₇×#2835 #14525841

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₁₇×#2835

Subgroups

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

380 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 1088

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)(19,22)(23,25)(26,27)(28,30)(29,31)(32,33)(34,35,38,40)(36,37,39,41);(20,24)(23,25)(26,27,29,31)(28,30,33,32)(34,36)(35,37)(38,39)(40,41);(18,19,21,22)(20,23,24,25)(26,28,29,33)(27,30,31,32)(34,37)(35,39)(36,40)(38,41);(18,20)(19,23)(21,24)(22,25)(26,27)(28,32)(29,31)(30,33)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946641, #16947227, D₁₇×#2835, …
maximal subgroup of	C₁₇×#12139, C₁₇×#12233, C₂×C₁₇×#2835, …
maximal normal subgroup of	C₁₇×#12139, C₁₇×#12233, C₂×C₁₇×#2835, …
maximal quotient of	C₁₇×#14627, C₁₇×#14635, C₁₇×#14647, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1567);