#72218947

order	4656
automorphism	?
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₃×C₉₇ ⋊ C₁₆
Sylow	C₉₇ ⋊ C₃⋊C₁₆
Sylow	C₃ ⋊ #13095525

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₉₇	C₁₆
prime radical	C₃×D₉₇	C₈
cosocle	C₃×#11715906	C₂
LCS	G ▷ C₃×C₉₇
UCS	C₁

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^4,3,97|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^12,f^b=f^47,f^c=f^75,f^d=f^96

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72218948, D₃×#13095525
maximal normal subgroup of	#72218948, D₃×#13095525

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, 3, 97]);;
gap> SetPower(coll, 1, F.2);;
gap> SetPower(coll, 2, F.3);;
gap> SetPower(coll, 3, F.4);;
gap> SetConjugate(coll, 5, 1, F.5^2);;
gap> SetConjugate(coll, 6, 1, F.6^12);;
gap> SetConjugate(coll, 6, 2, F.6^47);;
gap> SetConjugate(coll, 6, 3, F.6^75);;
gap> SetConjugate(coll, 6, 4, F.6^96);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);