#72218903

order	4624
automorphism	?
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Sylow

C₁₇² ⋊ C₁₆

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₇²	C₁₆
prime radical	C₁₇⋊D₁₇	C₈
cosocle	#72213369	C₂
LCS	G ▷ C₁₇²
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^4,17^2|a^2=b,b^2=c,c^2=d,e^a=e^3,e^b=e^9,e^c=e^13,e^d=e^16,f^a=e^6f^12,f^b=e^5f^8,f^c=f^13,f^d=f^16

Conjugacy classes & character table

34 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72218904
maximal normal subgroup of	#72218904

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 17, 17]);;
gap> SetPower(coll, 1, F.2);;
gap> SetPower(coll, 2, F.3);;
gap> SetPower(coll, 3, F.4);;
gap> SetConjugate(coll, 5, 1, F.5^3);;
gap> SetConjugate(coll, 5, 2, F.5^9);;
gap> SetConjugate(coll, 5, 3, F.5^13);;
gap> SetConjugate(coll, 5, 4, F.5^16);;
gap> SetConjugate(coll, 6, 1, F.5^6*F.6^12);;
gap> SetConjugate(coll, 6, 2, F.5^5*F.6^8);;
gap> SetConjugate(coll, 6, 3, F.6^13);;
gap> SetConjugate(coll, 6, 4, F.6^16);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);