Finite Group Databasebeta

C2×#22592302 #32165304

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

Aliases

direct productC2×#22592302

Splittings

SylowC71 ⋊ C2×#2461

Subgroups

subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
Fitting, prime radicalC2×#392×C71C2
socleC24×C71C24
hypercenterC2×#392D71
hypocenterC71C2×#2461
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#392

3786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

1616 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 337420);