C₁₇×#2825 #14525831

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₁₇×#2825

Subgroups

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

522 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 168 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)(19,22)(23,25)(26,27)(28,31)(29,30)(32,33)(34,35,38,39)(36,40,41,37);(20,24)(23,25)(27,30)(28,32)(36,41)(37,40);(18,19)(20,23)(21,22)(24,25)(26,27)(28,33)(29,30)(31,32)(34,36)(35,37)(38,41)(39,40);(18,20)(19,23)(21,24)(22,25)(26,28)(27,31)(29,32)(30,33)(34,37)(35,36)(38,40)(39,41)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2825, #17240719, #17240761, …
maximal subgroup of	C₂×C₁₇×#2825, C₁₇×#36670, C₁₇×#36676, …
maximal normal subgroup of	C₂×C₁₇×#2825, C₁₇×#36670, C₁₇×#36676, …
maximal quotient of	C₁₇×#14621, C₁₇×#14637, C₁₇×#14642, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1557);