#72257983

order	6728
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Sylow

C₂₉² ⋊ C₂×C₄

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₉²	C₂×C₄
prime radical	D₂₉²	C₂
cosocle	C₂₉⋊D₂₉	C₂²
LCS	G ▷ C₂₉²
UCS	C₁

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 58

Polycyclic presentation:

2^3,29^2|b^2=c,d^a=d^28,d^b=d^17,d^c=d^28,e^a=d^20e,e^b=e^17,e^c=e^28

Conjugacy classes & character table

134 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72257984
maximal normal subgroup of	#72257984

GAP

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

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e");;
gap> coll := SingleCollector(F, [2, 2, 2, 29, 29]);;
gap> SetPower(coll, 2, F.3);;
gap> SetConjugate(coll, 4, 1, F.4^28);;
gap> SetConjugate(coll, 4, 2, F.4^17);;
gap> SetConjugate(coll, 4, 3, F.4^28);;
gap> SetConjugate(coll, 5, 1, F.4^20*F.5);;
gap> SetConjugate(coll, 5, 2, F.5^17);;
gap> SetConjugate(coll, 5, 3, F.5^28);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);