C₁₇×#2388 #14525394

order	2176
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#2388

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
socle	C₂³×C₁₇	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

944 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 248 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)(18,19)(20,21)(26,27)(28,31)(29,30)(32,33);(22,23)(24,25)(27,30)(31,33);(19,21)(23,25);(26,28,29,32)(27,31,30,33)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16929294, #16929299, #16944648, …
maximal subgroup of	C₁₇×#9009, C₁₇×#9010, C₁₇×#11725, …
maximal normal subgroup of	C₁₇×#9009, C₁₇×#9010, C₁₇×#11725, …
maximal quotient of	C₁₇×#13839, C₁₇×#13844, C₁₇×#13851, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1120);