Finite Group Databasebeta

C2×C42×D284 #32155645

order18176
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C42×D284

Splittings

FittingC2×C43×C71 ⋊ C2
SylowC71 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC22×C42C2×D71
commutatorC2×C71C23×C42
FrattiniC23C24×D71
FittingC2×C43×C71C2
socleC24×C71C24
prime radicalC23×D284C22
cosocleC23×C71C25
hypercenterC2×C43D71
hypocenterC71C2×C42×D4
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C42 ◁ C2×C43

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

4640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 327761);