C₁₇×#3292 #14526298

order	2176
nilpotency class	3
isoclinism	isoclinic class of #3290
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#3292

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ G

476 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 184 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 — 4 generators on 33 points:

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

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947717, #16947727, #16948093, …
maximal subgroup of	C₁₇×#12310, C₁₇×#12312, C₁₇×#12366, …
maximal normal subgroup of	C₁₇×#12310, C₁₇×#12312, C₁₇×#12366, …
maximal quotient of	C₁₇×#19885, C₁₇×#19893, C₁₇×#19898, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2024);