Finite Group Databasebeta

#34029898

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

FittingC2×#120×C73 ⋊ C4
SylowC73 ⋊ #33348

Subgroups

subgroupG/H
centerC2C2×D73⋊#99
commutatorC23×C73C23×C4
FrattiniC23C23×#64408
FittingC2×#120×C73C4
socleC2×C73C22×#99
prime radical#22623560C2
cosocleC2×C22⋊D73C24
hypercenterC2×#120#64408
hypocenterC73#33348
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#120

1410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1168

Polycyclic presentation:

2^8,73|a^2=f,b^a=be,e^a=eg,g^a=gh,i^a=i^27,f^b=fg,d^c=dh,i^c=i^72,f^e=fh,i^f=i^72

Conjugacy classes & character table

550 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1113482);