Finite Group Databasebeta

C2×#22613356 #33254393

order18688
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22613356

Splittings

FittingC22×C22⋊Q8×C73 ⋊ C2
SylowC73 ⋊ C2×#2415

Subgroups

subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC22×C22⋊Q8×C73C2
socleC24×C73C24
prime radicalC23×C22⋊D73C22
hypercenterC22×C22⋊Q8D73
hypocenterC73C2×#2415
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

3526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 337977);