Finite Group Databasebeta

C2×#22592001 #32164875

order18176
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22592001

Splittings

SylowC71 ⋊ C2×#2437

Subgroups

subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC23×C22⋊C4×C71C2
socleC24×C71C24
prime radicalC26×C71C22
hypercenterC23×C22⋊C4D71
hypocenterC71C2×#2437
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C23×C22⋊C4

4926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 336991);