C₁₇×#2760 #14525766

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#2760

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₁₇×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

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

normal subgroups only

This group has 520 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)(19,22)(20,24)(26,27,30,28)(29,32,33,31)(34,35)(36,40)(37,38)(39,41);(19,22)(23,25)(27,28)(29,33)(35,38)(36,41);(18,19,21,22)(20,23,24,25)(26,28,30,27)(29,32,33,31)(34,36)(35,39)(37,41)(38,40);(18,20)(19,23)(21,24)(22,25)(26,29)(27,31)(28,32)(30,33)(34,35)(36,39)(37,38)(40,41)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946937, #16947421, #17242646, …
maximal subgroup of	C₁₇×#12187, C₁₇×#12263, C₁₇×#36776, …
maximal normal subgroup of	C₁₇×#12187, C₁₇×#12263, C₁₇×#36776, …
maximal quotient of	C₁₇×#14375, C₁₇×#14508, C₁₇×#14572, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1492);