C₁₇×#2309 #14525315

order	2176
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

direct product

C₁₇×#2309

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂³×D₄×C₁₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

1104 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 360 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 — 4 generators on 33 points:

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

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16927829, #16927832, #16932233, …
maximal subgroup of	C₁₇×#8748, C₁₇×#8749, C₁₇×#9497, …
maximal normal subgroup of	C₁₇×#8748, C₁₇×#8749, C₁₇×#9497, …
maximal quotient of	C₁₇×#13775, C₁₇×#13785, C₁₇×#13795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1041);