C₁₇×#1437 #14524443

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₇×#1437

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂³
commutator	C₂²	C₂×C₄²×C₁₇
Frattini, cosocle	C₂⁴	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

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

normal subgroups only

This group has 828 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) = 1088

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921349, #16925834, D₁₇×#1437, …
maximal subgroup of	C₁₇×#7213, C₁₇×#8346, C₂×C₁₇×#1437, …
maximal normal subgroup of	C₁₇×#7213, C₁₇×#8346, C₂×C₁₇×#1437, …
maximal quotient of	C₁₇×#7554, C₁₇×#7555, C₁₇×#7556, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 169);