C₁₇×#3549 #14526555

order	2176
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₇ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

direct product

C₁₇×#3549

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ G

1258 conjugacy classes of subgroups; only the 768 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 768 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) = 544

A minimal faithful permutation representation — 5 generators on 33 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926678, #16926879, #16950179, …
maximal subgroup of	C₁₇×#8491, C₁₇×#8530, C₁₇×#12769, …
maximal normal subgroup of	C₁₇×#8491, C₁₇×#8530, C₁₇×#12769, …
maximal quotient of	C₁₇×#34368, C₁₇×#34415, C₁₇×#34485, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2281);