C₁₇×#2621 #14525627

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#2621

Subgroups

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

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

normal subgroups only

This group has 528 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) = 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)(22,23,24,25)(27,31)(32,34)(33,39)(40,41);(19,21)(26,27)(28,34)(29,33)(30,31)(32,36)(35,41)(37,40)(38,39);(18,19)(20,21)(22,23)(24,25)(26,28,30,36)(27,32,31,34)(29,37,38,35)(33,41,39,40);(26,29,30,38)(27,33,31,39)(28,35,36,37)(32,40,34,41)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16930348, #16930353, #16944513, …
maximal subgroup of	C₁₇×#9195, C₁₇×#9196, C₁₇×#11694, …
maximal normal subgroup of	C₁₇×#9195, C₁₇×#9196, C₁₇×#11694, …
maximal quotient of	C₁₇×#14258, C₁₇×#14261, C₁₇×#14274, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1353);