Finite Group Databasebeta

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#34061463

order19072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

FittingAGL(1,ℤ/8)×C149 ⋊ C4
SylowC149 ⋊ #2955

Subgroups

subgroupG/H
centerC2C2×D4×#10597010
commutatorC4×C149C23×C4
FrattiniC4C23×#10597010
FittingAGL(1,ℤ/8)×C149C4
socleC2×C149C2×C4×D4
prime radical#23750421C2
cosocleC4×D149C24
hypercenterAGL(1,ℤ/8)#10597010
hypocenterC149#2955
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4768

Polycyclic presentation:

2^7,149|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^44,e^b=eg,h^c=h^105,h^f=h^148

Conjugacy classes & character table

451 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 21282);