Finite Group Databasebeta

C2×#22590276 #32151208

order18176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22590276

Splittings

SylowC71 ⋊ C2×#2188

Subgroups

subgroupG/H
centerC23C2×D568
commutator, cosocleC2×C8×C71C24
FrattiniC2×C8C23×D71
FittingC2×C22⋊C16×C71C2
socleC23×C71C2×D8
prime radicalC24×C71D8
hypercenterC2×C22⋊C16D71
hypocenterC71C2×#2188
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

1126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2858 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 323324);