C₁₇×#2785 #14525791

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₄³

Aliases

direct product

C₁₇×#2785

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

428 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 176 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)(18,19,22,20)(21,24,25,23)(26,27)(28,31)(29,30)(32,33)(35,36)(39,40);(19,20)(21,25)(27,29)(31,32)(34,35,38,36)(37,40,41,39);(18,20,22,19)(21,24,25,23)(26,28,30,33)(27,31,29,32)(34,36,38,35)(37,40,41,39);(18,21,22,25)(19,23,20,24)(26,29,30,27)(28,32,33,31)(34,37)(35,39)(36,40)(38,41)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946683, #16947269, #17243280, …
maximal subgroup of	C₁₇×#12145, C₁₇×#12239, C₁₇×#36796, …
maximal normal subgroup of	C₁₇×#12145, C₁₇×#12239, C₁₇×#36796, …
maximal quotient of	C₁₇×#14399, C₁₇×#14476, C₁₇×#14589, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1517);