Finite Group Databasebeta

C2×#22588360 #31996989

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22588360

Splittings

SylowC71 ⋊ C2×#1806

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×C4×#41×C71C2
socleC23×C71C2×C22⋊C4
prime radicalC22×#41×C71C22
cosocleC22×C4×C71C24
hypercenterC2×C4×#41D71
hypocenterC71C2×#1806
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

1618 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, 169105);