Finite Group Databasebeta

C2×#22602225 #32905894

order18176
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#22602225

Splittings

SylowC71 ⋊ C2×#3509

Subgroups

subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#536×C71C2
socleC23×C71C25
prime radicalC22×#41×C71C22
hypercenterC2×#536D71
hypocenterC71C2×#3509
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#536

7022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1078010);