C₁₇×#2200 #14525206

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2199
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2200

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂³×C₁₇
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂×D₄×C₁₇ ◁ G

260 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 56 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)(20,26)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33);(18,20,22,27)(19,23,25,30)(21,28,29,33)(24,26,31,32);(20,27)(21,29)(23,30)(26,32)

Conjugacy classes & character table

289 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2200, #17188372, #17188384, …
maximal subgroup of	C₂×C₁₇×#2200, C₁₇×#33550, C₁₇×#33551, …
maximal normal subgroup of	C₂×C₁₇×#2200, C₁₇×#33550, C₁₇×#33551, …
maximal quotient of	C₁₇×#12093, C₁₇×#12094, C₁₇×#12099, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 932);