C₁₇×#2551 #14525557

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#2551

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

556 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 2176

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)(19,20)(26,27,30,33)(28,32,29,31);(18,19,21,20)(22,23,24,25)(26,28,30,29)(27,31,33,32);(22,23)(24,25)(26,28,30,29)(27,31,33,32);(18,20,21,19)(26,29,30,28)(27,32,33,31)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16937331, #16937336, #16937341, …
maximal subgroup of	C₁₇×#10348, C₁₇×#10349, C₁₇×#10350, …
maximal normal subgroup of	C₁₇×#10348, C₁₇×#10349, C₁₇×#10350, …
maximal quotient of	C₁₇×#13910, C₁₇×#14005, C₁₇×#14053, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1283);