C₁₇×#2643 #14525649

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

Aliases

direct product

C₁₇×#2643

Subgroups

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

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

normal subgroups only

This group has 462 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,23)(20,21,24,25)(27,30)(31,32)(34,35)(36,39)(37,40)(38,41);(19,23)(20,24)(26,27,29,30)(28,31,33,32)(34,36)(35,38)(37,41)(39,40);(18,20)(19,21)(22,24)(23,25)(26,27)(28,32)(29,30)(31,33)(34,36)(35,39)(37,41)(38,40);(18,21)(19,24)(20,23)(22,25)(26,28)(27,31)(29,33)(30,32)(34,35)(36,38)(37,40)(39,41)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2643, #17200854, #17201015, …
maximal subgroup of	C₂×C₁₇×#2643, C₁₇×#34570, C₁₇×#34584, …
maximal normal subgroup of	C₂×C₁₇×#2643, C₁₇×#34570, C₁₇×#34584, …
maximal quotient of	C₁₇×#14259, C₁₇×#14265, C₁₇×#14331, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1375);