C₁₇×#2274 #14525280

order	2176
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₇×#2274

Subgroups

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

696 conjugacy classes of subgroups; only the 520 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 520 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)(22,23,25,24)(26,27,30,28)(29,32,33,31);(18,19,20,21)(22,24,25,23)(27,28)(31,32);(26,28,30,27)(29,32,33,31);(26,29)(27,31)(28,32)(30,33)

Conjugacy classes & character table

1156 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#16927786, #16931764, #16931774, …
maximal subgroup of	C₁₇×#8735, C₁₇×#9408, C₁₇×#9410, …
maximal normal subgroup of	C₁₇×#8735, C₁₇×#9408, C₁₇×#9410, …
maximal quotient of	C₁₇×#13749, C₁₇×#13750, C₁₇×#13776, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1006);