C₁₇×#2616 #14525622

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#2616

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂²×#41×C₁₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

816 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 232 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) = 33
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16934639, #16934667, #17007547, …
maximal subgroup of	C₁₇×#9931, C₁₇×#9935, C₁₇×#18230, …
maximal normal subgroup of	C₁₇×#9931, C₁₇×#9935, C₁₇×#18230, …
maximal quotient of	C₁₇×#14258, C₁₇×#14264, C₁₇×#14300, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1348);