Finite Group Databasebeta

C2×#22587809 #31980041

order18176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22587809

Splittings

SylowC71 ⋊ C2×#1686

Subgroups

subgroupG/H
centerC23#14556099
commutator, cosocleC42×C71C24
FrattiniC42C23×D71
FittingC2×#492×C71C2
socleC23×C71#121
prime radicalC2×#127×C71C22
hypercenterC2×#492D71
hypocenterC71C2×#1686
LCSG ▷ C42×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

1586 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 152157);