C₁₇×#2128 #14525134

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2127
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₁₇×#2128

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	C₂×#99
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×D₄	C₂³×C₁₇
prime radical	C₁₇×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

270 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 272

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

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16949870, #16949885, #16949925, …
maximal subgroup of	C₁₇×#12711, C₁₇×#12714, C₁₇×#12722, …
maximal normal subgroup of	C₁₇×#12711, C₁₇×#12714, C₁₇×#12722, …
maximal quotient of	C₁₇×#11433, C₁₇×#11450, C₁₇×#11480, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 860);