Finite Group Databasebeta

C2×#22590328 #32151458

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

Aliases

direct productC2×#22590328

Splittings

SylowC71 ⋊ C2×#2197

Subgroups

subgroupG/H
centerC22#17986185
commutator, cosocleC2×D4×C71C24
FrattiniC2×D4C23×D71
Fitting, prime radicalC2×B(4,𝔽2)×C71C2
socleC22×C71B(4,𝔽2)
hypercenterC2×B(4,𝔽2)D71
hypocenterC71C2×#2197
LCSG ▷ C2×D4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×B(4,𝔽2)

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 323574);