C₁₇×#2230 #14525236

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2230
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#2230

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#476
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

126 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 60 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)(19,22)(20,28,30,25)(21,23)(26,27)(29,31,32,33);(18,19,21,22,24,27,23,26)(20,25,29,31,30,28,32,33);(18,20)(19,25)(21,29)(22,31)(23,32)(24,30)(26,33)(27,28)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16948082, #16948087, #16948092, …
maximal subgroup of	C₁₇×#12364, C₁₇×#12365, C₁₇×#12366, …
maximal normal subgroup of	C₁₇×#12364, C₁₇×#12365, C₁₇×#12366, …
maximal quotient of	C₁₇×#12823, C₁₇×#12950, C₁₇×#13116, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 962);