C₁₇×#2619 #14525625

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₁₇×#2619

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

728 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 1088

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)(22,23,24,25)(26,27)(28,31)(29,30)(32,33);(19,21)(27,30)(31,32);(18,19)(20,21)(22,23)(24,25)(26,27)(28,32)(29,30)(31,33);(26,28,29,33)(27,31,30,32)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16930358, #16930363, #16944509, …
maximal subgroup of	C₁₇×#9197, C₁₇×#9198, C₁₇×#11693, …
maximal normal subgroup of	C₁₇×#9197, C₁₇×#9198, C₁₇×#11693, …
maximal quotient of	C₁₇×#14257, C₁₇×#14260, C₁₇×#14272, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1351);