Finite Group Databasebeta

C2×#22586228 #31887592

order18176
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22586228

Splittings

SylowC71 ⋊ C2×#1298

Subgroups

subgroupG/H
centerC22×C4(C2×D71)⋊C4
commutatorC2×C4×C71C2×C42
FrattiniC23×C4C22×D71
FittingC22×C22⋊C8×C71C2
socleC23×C71#95
prime radicalC25×C71Q8
cosocleC23×C4×C71C23
hypercenterC22×C22⋊C8D71
hypocenterC71C2×#1298
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

938 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, 59708);